Control apparatus, control method, and engine control unit

ABSTRACT

A control apparatus which is capable of compensating for a control error properly and quickly even under a condition where the control error is temporarily increased e.g. by degradation of reliability of the detection results of reference parameters other than controlled variables, thereby making it possible to ensure a high accuracy of control. An air-fuel ratio controller of the control apparatus calculates modified errors by multiplying e.g. an air-fuel ratio error estimated value by link weight functions, calculates basic local correction values such that the modified errors become equal to 0; calculates local correction values by multiplying the basic local correction values and the like by the link weight functions; calculates corrected valve lift by adding a lift correction value, which is the total sum of the local correction values, to a value of valve lift; calculates a first estimated intake air amount for feedforward control of an air-fuel ratio, based on the corrected valve lift; calculates an air-fuel ratio correction coefficient for feedback control of the air-fuel ratio; and calculates a fuel injection amount based on these.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a control apparatus that calculates acontrol input based on a value calculated by a feedback control methodand a value calculated by a feedforward control method, to therebycontrol a controlled variable using the control input, a control method,and an engine control unit.

2. Description of the Related Art

Conventionally, as a control apparatus of this kind, the presentassignee has already proposed a control apparatus disclosed in JapaneseLaid-Open Patent Publication (Kokai) No. 2005-315161. This controlapparatus controls the air-fuel ratio of a mixture in an internalcombustion engine as a controlled variable, based on a fuel amount as acontrol input, and is comprised of an air flow sensor that detects theflow rate of air flowing through an intake passage of the engine, apivot angle sensor that detects a valve lift, a cam angle sensor thatdetects the phase of a camshaft for actuating an intake valve to openand close the same, relative to a crankshaft (hereinafter referred to as“the cam phase”), and a crank angle sensor. Further, the engine includesthe intake passage having a large diameter, as well as a variable valvelift mechanism and a variable cam phase mechanism as variable intakemechanisms. In the engine, the valve lift and the cam phase are changedas desired by the variable valve lift mechanism and the variable camphase mechanism, respectively, whereby the amount of intake air ischanged as desired.

In the above control apparatus, as an intake air amount, a firstestimated intake air amount is calculated in a low-load region based onthe valve lift and the cam phase, and in a high-load region, a secondestimated intake air amount is calculated based on the flow rate of air.In a load region between the low-load region and the high-load region, aweighted average value of the first and second estimated intake airamounts is calculated. This is because in the low-load region where thereliability of the second estimated intake air amount is lower than thatof the first estimated intake air amount due to the large diameter ofthe intake system of the engine, the first estimated intake air amounthigher in reliability is employed, whereas in the high-load region inwhich occurs a state opposite to the above state in the low-load region,the second estimated intake air amount higher in reliability isemployed. Further, a basic fuel amount is calculated as a value for usein feedforward control of the air-fuel ratio based on the thuscalculated intake air amount, and an air-fuel ratio correctioncoefficient is calculated with a predetermined feedback controlalgorithm such that the air-fuel ratio is caused to converged to atarget air-fuel ratio. A final fuel amount is calculated based on avalue obtained by multiplying a basic fuel amount by the air-fuel ratiocorrection coefficient. Then, this amount of fuel is injected intocylinders via fuel injection valves, whereby the air-fuel ratio isaccurately controlled such that it becomes equal to the target air-fuelratio.

According to the above-described control apparatus, when detectionsignals from the pivot angle sensor, the cam angle sensor, and the crankangle sensor drift due to changes in temperature, for example, or whenthe static characteristics of a variable valve lift mechanism and avariable cam phase mechanism (i.e. the relationship between the valvelift and the cam phase with respect to the control input) are changed bywear of components of the two variable mechanisms, attachment of stain,and play produced by aging, the reliability of the results of detectionby the sensors lowers, which can result in a temporary increase in thecontrol error of the air-fuel ratio. More specifically, when the firstestimated intake air amount ceases to represent an actual intake airamount, and deviates from the actual intake air amount, there is a fearthat the fuel amount cannot be properly calculated as a control input inthe low load region where the first estimated intake air amount is usedas the control input. In such a case, the difference between theair-fuel ratio as the controlled variable and the target air-fuel ratio,that is, the control error increases. Although the control error can becompensated for by the air-fuel ratio correction coefficient in a steadystate since the air-fuel ratio correction coefficient is calculated withthe predetermined feedback control algorithm, it takes time before thecontrol error is compensated for by the air-fuel ratio correctioncoefficient. Therefore, e.g. when the control error temporarilyincreases, the accuracy of control is temporarily degraded, whichresults in unstable combustion and degraded combustion efficiency. Theproblem described above is liable to be more conspicuous in a transientoperating state of the engine.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a control apparatus,a control method, and an engine control unit which are capable ofcompensating for a control error properly and quickly even under acondition where the control error is temporarily increased e.g. by thedegraded reliability of the results of detection of reference parametersother than controlled variables, thereby making it possible to ensurehigh-level accuracy of control.

To attain the above object, in a first aspect of the present invention,there is provided a control apparatus for controlling a controlledvariable of a controlled object by a control input, comprisingcontrolled variable-detecting means for detecting the controlledvariable, reference parameter-detecting means for detecting a referenceparameter of the controlled object other than the controlled variable ofthe controlled object, target controlled variable-setting means forsetting a target controlled variable serving as a target to which thecontrolled variable is controlled, and control input-calculating meansfor calculating a first input value for feedforward control of thecontrolled variable, according to the reference parameter, using acorrelation model representative of a correlation between the referenceparameter and the first input value, calculating a second input valuefor performing feedback control of the controlled variable such that thecontrolled variable is caused to converge to the target controlledvariable, with a predetermined feedback control algorithm, andcalculating the control input based on the first input value and thesecond input value, wherein the control input-calculating meanscomprises error parameter-calculating means for calculating an errorparameter indicative of a control error to be compensated for by thefirst input value, based on the controlled variable and the targetcontrolled variable, model-modifying means for calculating a pluralityof modification values respectively associated with a plurality ofregions formed by dividing a region within which the reference parameteris variable, with a predetermined control algorithm, such that the errorparameter becomes equal to a predetermined target value, and modifyingthe correlation model using the plurality of modification values, andfirst input value-calculating means for calculating the first inputvalue using the modified correlation model.

In the case of this control apparatus which calculates the first inputvalue for feedforward control of the controlled variable according tothe reference parameter, using the correlation model representative ofthe correlation between the reference parameter and the first inputvalue, a control error occurs not only due to a disturbance but also dueto incapability of the correlation model for properly representing anactual correlation between the reference parameter and the first inputvalue, e.g. due to the degraded reliability of the detection results ofthe reference parameter, in other words, due to deviation of thecorrelation model from the actual correlation therebetween, and an errorparameter is calculated so as to represent the control error. In thiscase, as described above, it takes time to compensate for the controlerror represented by the error parameter if the compensation is to becarried out using the second input value parameter calculated with afeedback control algorithm.

In contrast, with the configuration of this control apparatus, the errorparameter indicative of the control error to be compensated for by thefirst input value is calculated based on the controlled variable and thetarget controlled variable, and the respective modification valuesassociated with the regions formed by dividing the region where thereference parameter is variable are calculated with the predeterminedcontrol algorithm, such that the error parameter becomes equal to thepredetermined target value. The correlation model is modified using themodification values, and the first input value is calculated using thethus modified correlation model. Thus, the first input value iscalculated using the correlation model modified for the plurality ofregions, on a region-by-region basis, such that the error parameterbecomes equal to the predetermined target value. Therefore, not onlywhen the control error is temporarily increased by a disturbance butalso under a condition where the correlation model has deviated from theactual correlation between the reference parameter and the first inputvalue due to the degraded reliability of the detection results of thereference parameter or a change in the dynamic characteristics of thecontrolled object, causing a temporary increase in the error parameter,i.e. the control error, it is possible to properly compensate for thecontrol error by the first input value calculated using the modifiedcorrelation model. Particularly, even when the deviation of thecorrelation model from the actual correlation between the referenceparameter and the first input value is different in respect of thedirection of change thereof between regions of the reference parameter,it is possible to properly modify the correlation model on anregion-by-region basis while coping with the deviation, thereby makingit possible to ensure a high-level capability of compensating for thecontrol error. In addition, by using an N (N is a natural number notsmaller than 2) dimensional map which is generally used in thefeedforward control method for representing the correlation between thereference parameter and the first input value, and a calculatingequation representing the correlation therebetween, for the correlationmodel, the control error indicated by the error parameter can becompensated for more quickly than in a case where the same iscompensated for by the second input value.

As described above, even under the condition where the control error istemporarily increased due to the degraded reliability of the detectionresults of the reference parameter or a change in the dynamiccharacteristics of the controlled object, it is possible to compensatefor the control error properly and quickly, thereby making it possibleto ensure high-level accuracy of control (It should be noted thatthroughout the specification, “correlation model” is not limited to aresponse surface model or a mathematical model but includes all modelswhich represent the correlation between the reference parameter and thefirst input value, such as the N (N is a natural number not smaller than2) dimensional map and a predetermined calculation algorithm. Further,“detection of a parameter” is not limited to direct detection of theparameter by a sensor, but includes calculation or estimation thereof.In addition thereto, “calculation of a parameter” is not limited tocalculation or estimation of the same, but includes direct detectionthereof by a sensor).

Preferably, the reference parameter-detecting means detects a pluralityof reference parameters as the reference parameter, and the correlationmodel is configured such that the correlation model is representative ofa relationship between the plurality of reference parameters and thefirst input value, the model-modifying means calculating the pluralityof modification values such that the plurality of modification valuesare associated with a region within which at least one of the pluralityof reference parameters is variable.

With the configuration of the preferred embodiment, the correlationmodel is configured such that it is indicative of the relationshipbetween the plurality of reference parameters and the first input value,and the modification values are calculated such that they are associatedwith a region where at least one of the reference parameters isvariable, while the first input value is calculated using thecorrelation model modified for the regions on a region-by-region basis,such that the error parameter becomes equal to the predetermined targetvalue. Therefore, even when the error parameter, i.e. the control erroris temporarily increased, due to deviation of the correlation model froman actual correlation between the reference parameters and the firstinput value, the control error can be properly compensated for by thefirst input value calculated using the modified correlation model.

Preferably, the model-modifying means calculates a plurality of firstmultiplication values by multiplying a difference between the errorparameter and the predetermined target value, by values of a respectiveplurality of predetermined functions, and calculates the plurality ofmodification values according to the plurality of first multiplicationvalues, respectively, the plurality of regions having adjacent regionsoverlapping each other, and the plurality of predetermined functions areassociated with the plurality of regions, respectively, and are set tovalues other than 0 only in the associated regions and to 0 in regionsother than the associated regions, such that in regions overlapping eachother, an absolute value of a total sum of values of the respectivefunctions associated with the overlapping regions becomes equal to anabsolute value of a maximum value of the functions.

With the configuration of the preferred embodiment, the predeterminedfunctions are associated with the regions, respectively, and set to thevalues other than 0 only in the associated regions and to 0 in regionsother than the associated regions, such that in the regions overlappingeach other, the absolute value of the total sum of the values of therespective functions associated with the overlapping regions becomesequal to the absolute value of the maximum value of the functions. Thefirst multiplication values are calculated by multiplying the differencebetween the error parameter and the predetermined target value, by therespective values of the thus set predetermined functions, and themodification values are calculated based on the first multiplicationvalues, respectively. This makes it possible to distribute thedifference between the error parameter and the predetermined targetvalue, to the modification values via the values of the predeterminedfunctions, thereby making it possible to properly modify, i.e. reducethe degrees of deviations of the correlation model in the respectiveregions by the modification values. In addition thereto, the absolutevalue of the total sum of the values of the functions associated withthe overlapping regions is set to be equal to the absolute value of themaximum value of the functions, so that the modification valuescalculated using the values of the thus set functions become valuescontinuous with each other, whereby even when the reference parametersare suddenly changed, it is possible to calculate the first input valuesmoothly and steplessly. Thus, even under a condition where the targetcontrolled variable and the environment of the controlled object aresuddenly changed to temporarily increase the control error, it ispossible to avoid a sudden improper change or a sudden stepped change inthe first input value, caused by the increase in the control error,thereby making it possible to enhance the accuracy and stability ofcontrol.

More preferably, the model-modifying means calculates a plurality ofsecond multiplication values by multiplying the plurality ofmodification values by values of the respective plurality ofpredetermined functions, respectively, and modifies the correlationmodel using a total sum of the plurality of second multiplicationvalues.

With the configuration of the preferred embodiment, the secondmultiplication values are calculated by multiplying the modificationvalues by the values of the respective predetermined functions, and thecorrelation model is modified using the total sum of the secondmultiplication values. In this case, as described above, themodification values are calculated such that they can modify, i.e.reduce the degrees of the deviations of the correlation model in theregions, respectively, so that the total sum of the secondmultiplication values can be calculated as a value obtained by asuccessive combination of the modification values thus calculated.Therefore, by modifying the correlation model using the thus calculatedvalue, even when the reference parameters are suddenly changed, it ispossible to calculate the first input value more smoothly andsteplessly, thereby making it possible to further enhance the accuracyand stability of control.

Preferably, the model-modifying means calculates a plurality ofmultiplication values by multiplying the plurality of modificationvalues by values of a respective plurality of predetermined functions,respectively, and modifies the correlation model using a total sum ofthe plurality of multiplication values, the plurality of regions havingadjacent regions overlapping each other, and the plurality ofpredetermined functions are associated with the plurality of regions,respectively, and are set to values other than 0 only in the associatedregions and to 0 in regions other than the associated regions, such thatin regions overlapping each other, an absolute value of a total sum ofvalues of the respective functions associated with the overlappingregions becomes equal to an absolute value of a maximum value of thefunctions.

With the configuration of the preferred embodiment, the predeterminedfunctions are associated with the regions, respectively, and are set tovalues other than 0 only in the associated regions and to 0 in regionsother than the associated regions, such that in regions overlapping eachother, the absolute value of the total sum of the values of therespective functions associated with the overlapping regions becomesequal to the absolute value of the maximum value of the functions, Themultiplication values are calculated by multiplying the modificationvalues by the values of the respective predetermined functions, and thecorrelation model is modified using the total sum of the multiplicationvalues. In this case, as described above, the modification values arecalculated such that they can modify, i.e. reduce the degrees of thedeviations of the correlation model in the regions, respectively, sothat the total sum of the second multiplication values can be calculatedas a value obtained by a successive combination of the modificationvalues thus calculated. Therefore, if the correlation model is modifiedusing the thus calculated value, even when the reference parameters aresuddenly changed, it is possible to calculate the first input value moresmoothly and steplessly, thereby making it possible to further enhancethe accuracy and stability of control.

Preferably, the controlled object is an internal combustion engine inwhich an amount of intake air drawn into a cylinder of the engine ischanged by a variable intake mechanism, as desired, the controlledvariable being an air-fuel ratio of a mixture in the engine, the controlinput being an amount of fuel to be supplied to the engine, thereference parameter including at least one of an operating conditionparameter indicative of an operating condition of the variable intakemechanism, and a rotational speed of the engine.

With the configuration of the preferred embodiment, the air-fuel ratioof the mixture is controlled by the amount of fuel to be supplied to theengine, and the amount of fuel to be supplied to the engine iscalculated based on the first input value and the second input value. Acorrelation model representative of the correlation between theoperating condition parameter and/or the rotational speed of the engine,and the first input value is modified using the modification values, andthe first input value is calculated using the modified correlationmodel. As a result, even when the correlation model has deviated fromthe actual correlation between the operating condition parameter and/orthe rotational speed of the engine, and the first input value, due tothe degraded reliability of the detection results of the operatingcondition parameter and/or the rotational speed of the engine, and achange in the dynamic characteristics of the engine, causing a temporaryincrease in the control error of the air-fuel ratio, it is possible tocompensate for the increased control error properly and quickly by thefirst input value calculated using the modified correlation model.Particularly, even when the direction of change in the deviation of thecorrelation model is different between regions of the operatingcondition parameter and/or the rotational speed of the engine, on aregion-by-region basis, it is possible to properly modify thecorrelation model on an region-by-region basis while coping with thedeviations. This makes it possible to ensure a high-level capability ofcompensating for the control error.

Preferably, the controlled object is a vehicle using the engine as adrive source thereof, the controlled variable being a first wheel speedof the vehicle, the control input being an output of the engine, thereference parameter including at least one of a second wheel speed otherthan the first wheel speed, a limit value of the output of the engine,and a rotational speed of the engine.

With the configuration of the preferred embodiment, the first wheelspeed of the vehicle is controlled by the output of the engine, and theoutput of the engine is calculated based on the first and second inputvalues. The correlation model representative of the correlation betweenat least one of the second wheel speed other than first wheel speed, thelimit value of the output of the engine, and the rotational speed of theengine, and the first input value is modified using the modificationvalues, and the first input value is calculated using the modifiedcorrelation model. Thus, even when the correlation model becomesincapable of properly representing the actual correlation between the atleast one of the second wheel speed, the limit value of the output ofthe engine, and the rotational speed of the engine, and the first inputvalue, due to unpredictable changes in conditions, such as ageddegradation of the output characteristics of the engine, variationsbetween individual engines, changes in the degree of wear of tires, andchanges in the frictional resistance of road surfaces, and hence thecontrol error is liable to temporarily increase, it is possible toproperly and quickly compensate for the control error just enough, bythe first input value calculated using the modified correlation model,thereby making it possible to suppress the increase in the controlerror. As a result, it is possible to ensure higher-level controlaccuracy of the wheel speed than by a gain schedule correction (ormodification) method. In short, a higher-level traction control can berealized.

To attain the above object, in a second aspect of the present invention,there is provided a method of controlling a controlled variable of acontrolled object by a control input, comprising:

a controlled variable-detecting step of detecting the controlledvariable;

a reference parameter-detecting step of detecting a reference parameterof the controlled object other than the controlled variable of thecontrolled object;

a target controlled variable-setting step of setting a target controlledvariable serving as a target to which the controlled variable iscontrolled; and

a control input-calculating step of calculating a first input value forfeedforward control of the controlled variable, according to thereference parameter, using a correlation model representative of acorrelation between the reference parameter and the first input value,calculating a second input value for performing feedback control of thecontrolled variable such that the controlled variable is caused toconverge to the target controlled variable, with a predeterminedfeedback control algorithm, and calculating the control input based onthe first input value and the second input value,

wherein the control input-calculating step comprises:

an error parameter-calculating step of calculating an error parameterindicative of a control error to be compensated for by the first inputvalue, based on the controlled variable and the target controlledvariable;

a model-modifying step of calculating a plurality of modification valuesrespectively associated with a plurality of regions formed by dividing aregion within which the reference parameter is variable, with apredetermined control algorithm, such that the error parameter becomesequal to a predetermined target value, and modifying the correlationmodel using the plurality of modification values; and

a first input value-calculating step of calculating the first inputvalue using the modified correlation model.

With the configuration of the second aspect of the present invention, itis possible to obtain the same advantageous effects as provided by thefirst aspect of the present invention.

Preferably, the reference parameter-detecting step includes detecting aplurality of reference parameters as the reference parameter, and thecorrelation model is configured such that the correlation model isrepresentative of a relationship between the plurality of referenceparameters and the first input value, the model-modifying step includingcalculating the plurality of modification values such that the pluralityof modification values are associated with a region within which atleast one of the plurality of reference parameters is variable.

Preferably, the model-modifying step includes calculating a plurality offirst multiplication values by multiplying a difference between theerror parameter and the predetermined target value, by values of arespective plurality of predetermined functions, and calculating theplurality of modification values according to the plurality of firstmultiplication values, respectively, the plurality of regions havingadjacent regions overlapping each other, and the plurality ofpredetermined functions are associated with the plurality of regions,respectively, and are set to values other than 0 only in the associatedregions and to 0 in regions other than the associated regions, such thatin regions overlapping each other, an absolute value of a total sum ofvalues of the respective functions associated with the overlappingregions becomes equal to an absolute value of a maximum value of thefunctions.

More preferably, the model-modifying step includes calculating aplurality of second multiplication values by multiplying the pluralityof modification values by values of the respective plurality ofpredetermined functions, respectively, and modifying the correlationmodel using a total sum of the plurality of second multiplicationvalues.

Preferably, the model-modifying step includes calculating a plurality ofmultiplication values by multiplying the plurality of modificationvalues by values of a respective plurality of predetermined functions,respectively, and modifying the correlation model using a total sum ofthe plurality of multiplication values, the plurality of regions havingadjacent regions overlapping each other, and the plurality ofpredetermined functions are associated with the plurality of regions,respectively, and are set to values other than 0 only in the associatedregions and to 0 in regions other than the associated regions, such thatin regions overlapping each other, an absolute value of a total sum ofvalues of the respective functions associated with the overlappingregions becomes equal to an absolute value of a maximum value of thefunctions.

Preferably, the controlled object is an internal combustion engine inwhich an amount of intake air drawn into a cylinder of the engine ischanged by a variable intake mechanism, as desired, the controlledvariable being an air-fuel ratio of a mixture in the engine, the controlinput being an amount of fuel to be supplied to the engine, thereference parameter including at least one of an operating conditionparameter indicative of an operating condition of the variable intakemechanism, and a rotational speed of the engine.

Preferably, the controlled object is a vehicle using the engine as adrive source thereof, the controlled variable being a first wheel speedof the vehicle, the control input being an output of the engine, thereference parameter including at least one of a second wheel speed otherthan the first wheel speed, a limit value of the output of the engine,and a rotational speed of the engine.

With the configurations of these preferred embodiments, it is possibleto obtain the same advantageous effects as provided by the preferredembodiments of the first aspect of the present invention.

To attain the object, in a third aspect of the present invention, thereis provided an engine control unit including a control program forcausing a computer to execute a method of controlling a controlledvariable of a controlled object by a control input,

wherein the control program causes the computer to detect the controlledvariable; detect a reference parameter of the controlled object otherthan the controlled variable of the controlled object; set a targetcontrolled variable serving as a target to which the controlled variableis controlled; and calculate a first input value for feedforward controlof the controlled variable, according to the reference parameter, usinga correlation model representative of a correlation between thereference parameter and the first input value, calculate a second inputvalue for performing feedback control of the controlled variable suchthat the controlled variable is caused to converge to the targetcontrolled variable, with a predetermined feedback control algorithm,and calculate the control input based on the first input value and thesecond input value, wherein when causing the computer to calculate thecontrol input, the control program causes the computer to calculate anerror parameter indicative of a control error to be compensated for bythe first input value, based on the controlled variable and the targetcontrolled variable; calculate a plurality of modification valuesrespectively associated with a plurality of regions formed by dividing aregion within which the reference parameter is variable, with apredetermined control algorithm, such that the error parameter becomesequal to a predetermined target value, and modifying the correlationmodel using the plurality of modification values; and calculate thefirst input value using the modified correlation model.

With the configuration of the third aspect of the present invention, itis possible to obtain the same advantageous effects as provided by thefirst aspect of the present invention.

Preferably, the control program causes the computer to detect aplurality of reference parameters as the reference parameter, thecorrelation model being configured such that the correlation model isrepresentative of a relationship between the plurality of referenceparameters and the first input value, and the control program causes thecomputer to calculate the plurality of modification values such that theplurality of modification values are associated with a region withinwhich at least one of the plurality of reference parameters is variable.

Preferably, the control program causes the computer to calculate aplurality of first multiplication values by multiplying a differencebetween the error parameter and the predetermined target value, byvalues of a respective plurality of predetermined functions, andcalculate the plurality of modification values according to theplurality of first multiplication values, respectively, the plurality ofregions having adjacent regions overlapping each other, and theplurality of predetermined functions are associated with the pluralityof regions, respectively, and are set to values other than 0 only in theassociated regions and to 0 in regions other than the associatedregions, such that in regions overlapping each other, an absolute valueof a total sum of values of the respective functions associated with theoverlapping regions becomes equal to an absolute value of a maximumvalue of the functions.

More preferably, the control program causes the computer to calculate aplurality of second multiplication values by multiplying the pluralityof modification values by values of the respective plurality ofpredetermined functions, respectively, and modify the correlation modelusing a total sum of the plurality of second multiplication values.

Preferably, the control program causes the computer to calculate aplurality of multiplication values by multiplying the plurality ofmodification values by values of a respective plurality of predeterminedfunctions, respectively, and modifying the correlation model using atotal sum of the plurality of multiplication values, the plurality ofregions having adjacent regions overlapping each other, and theplurality of predetermined functions are associated with the pluralityof regions, respectively, and are set to values other than 0 only in theassociated regions and to 0 in regions other than the associatedregions, such that in regions overlapping each other, an absolute valueof a total sum of values of the respective functions associated with theoverlapping regions becomes equal to an absolute value of a maximumvalue of the functions.

Preferably, the controlled object is an internal combustion engine inwhich an amount of intake air drawn into a cylinder of the engine ischanged by a variable intake mechanism, as desired, the controlledvariable being an air-fuel ratio of a mixture in the engine, the controlinput being an amount of fuel to be supplied to the engine, thereference parameter including at least one of an operating conditionparameter indicative of an operating condition of the variable intakemechanism, and a rotational speed of the engine.

Preferably, the controlled object is a vehicle using the engine as adrive source thereof, the controlled variable being a first wheel speedof the vehicle, the control input being an output of the engine, thereference parameter including at least one of a second wheel speed otherthan the first wheel speed, a limit value of the output of the engine,and a rotational speed of the engine.

With the configurations of these preferred embodiments, it is possibleto obtain the same advantageous effects as provided by the preferredembodiments of the first aspect of the present invention.

The above and other objects, features, and advantages of the presentinvention will become more apparent from the following detaileddescription taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an internal combustion engine to whichis applied a control apparatus according to a first embodiment of thepresent invention;

FIG. 2 is a schematic block diagram of the control apparatus;

FIG. 3 is a schematic cross-sectional view of a variable intakevalve-actuating mechanism and an exhaust valve-actuating mechanism ofthe engine;

FIG. 4 is a schematic cross-sectional view of a variable valve liftmechanism of the variable intake valve-actuating mechanism;

FIG. 5A is a diagram showing a lift actuator in a state in which a shortarm thereof is in a maximum lift position;

FIG. 5B is a diagram showing the lift actuator in a state in which theshort arm thereof is in a zero position;

FIG. 6A is a diagram showing an intake valve placed in an open statewhen a lower link of the variable valve lift mechanism is in a maximumlift position;

FIG. 6B is a diagram showing the intake valve placed in a stopped statewhen the lower link of the variable valve lift mechanism is in the zerolift position;

FIG. 7 is a diagram showing a valve lift curve (solid line) of theintake valve obtained when the lower link of the variable valve liftmechanism is in the maximum lift position, and a valve lift curve(two-dot chain line) of the intake valve obtained when the lower link ofthe variable valve lift mechanism is in the zero lift position;

FIG. 8 is a schematic diagram of a variable cam phase mechanism;

FIG. 9 is a diagram showing a valve lift curve (solid line) obtainedwhen a cam phase is set to a most retarded value by the variable camphase mechanism, and a valve lift curve (two-dot chain line) obtainedwhen the cam phase is set to a most advanced value by the variable camphase mechanism;

FIG. 10 is a schematic block diagram of an air-fuel ratio controller;

FIG. 11 is a diagram showing an example of a map for use in calculatinga basic estimated intake air amount;

FIG. 12 is a diagram showing an example of a map for use in calculatinga correction coefficient;

FIG. 13 is a diagram showing an example of a map for use in calculatinga transition coefficient;

FIG. 14 is a diagram showing an example of a map for use in calculatinga target air-fuel ratio;

FIG. 15 is a diagram showing the correlation between the basic estimatedintake air amount, a valve lift, and engine speed;

FIG. 16 is a diagram showing a state in which a lift error is caused byan offset of a calculated value of the valve lift with respect to theactual value thereof;

FIG. 17 is a diagram showing a state in which a lift error is caused bya change in dynamic characteristics of the variable valve liftmechanism;

FIG. 18 is a diagram showing the relationship between an amount ofchange in the basic estimated intake air amount and an amount of changein the valve lift;

FIG. 19 is a schematic block diagram of a lift correctionvalue-calculating section;

FIG. 20 is a diagram showing an example of a map for use in calculatinglink weight functions;

FIG. 21 is a diagram showing an example of a map for use in calculatinga basic error weight;

FIG. 22 is a diagram showing an example of a map for use in calculatingan error weight correction coefficient;

FIG. 23 is a diagram showing an example of a map for use in calculatinga basic sensitivity;

FIG. 24 is a diagram showing an example of a map for use in calculatinga sensitivity correction coefficient;

FIG. 25 is a flowchart of a control process executed at a controlperiod;

FIG. 26 is a flowchart of an air-fuel ratio control process;

FIG. 27 is a flowchart of a process for calculating a basic fuelinjection amount;

FIG. 28 is a flowchart of a control process executed at a controlperiod;

FIG. 29 is a flowchart of a process for calculating a corrected valvelift;

FIG. 30 is a flowchart of a variable mechanism control process;

FIG. 31 is a diagram showing an example of a map for use in calculatinga target valve lift during the start of the engine;

FIG. 32 is a diagram showing an example of a map for use in calculatinga target cam phase during the start of the engine;

FIG. 33 is a diagram showing an example of a map for use in calculatingthe target valve lift during catalyst warmup control;

FIG. 34 is a diagram showing an example of a map for use in calculatingthe target cam phase during catalyst warmup control;

FIG. 35 is a diagram showing an example of a map for use in calculatingthe target valve lift during normal operation of the engine;

FIG. 36 is a diagram showing an example of a map for use in calculatingthe target cam phase during normal operation of the engine;

FIG. 37 is a timing diagram showing an example of a result of air-fuelratio control executed by the control apparatus according to the firstembodiment;

FIG. 38 is a timing diagram showing a comparative example of a result ofair-fuel ratio control, obtained when a lift correction value is held at0;

FIG. 39 is a diagram showing another example of the map for use incalculating the link weight functions;

FIG. 40 is a schematic block diagram of an air-fuel ratio controller ofa control apparatus according to a second embodiment of the presentinvention;

FIG. 41 is a schematic block diagram of a lift correctionvalue-calculating section;

FIG. 42 is a diagram showing an example of the map for use incalculating the link weight functions;

FIG. 43 is a diagram which is useful in explaining a method ofcalculating the link weight functions;

FIG. 44 is a diagram which is useful in explaining the method ofcalculating the link weight functions;

FIG. 45 is a schematic block diagram of a control apparatus according toa third embodiment of the present invention;

FIG. 46 is a schematic block diagram of a traction controller;

FIG. 47 is a diagram showing an example of a map for use in calculatinga maximum torque and a minimum torque;

FIG. 48 is a diagram showing an example of a map for use in calculatinga normalization demand driving force;

FIG. 49 is a schematic block diagram of a torque correctionvalue-calculating section;

FIG. 50 is a diagram showing an example of a map for use in calculatinglink weight functions;

FIG. 51 is a diagram showing an example of a map for use in calculatingan error weight;

FIG. 52 is a diagram showing an example of a map for use in calculatinga torque correction sensitivity;

FIG. 53 is a timing diagram showing an example of results of tractioncontrol executed by the control apparatus according to the thirdembodiment; and

FIG. 54 is a timing diagram showing an example of results of thetraction control, obtained when a torque correction value=1 holds forcomparison with the FIG. 53 example.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Hereafter, a control apparatus according to a first embodiment of thepresent invention will be described with reference to the drawings. Asshown in FIG. 2, the control apparatus 1 includes an ECU 2. As describedhereinafter, the ECU 2 carries out control processes, such as anair-fuel ratio control process, depending on operating conditions of aninternal combustion engine, which is a controlled object.

Referring to FIGS. 1 and 3, an internal combustion engine (hereinaftersimply referred to as “the engine”) 3 is an in-line four-cylindergasoline engine having four pairs of cylinders 3 a and pistons 3 b (onlyone pair of which is shown), and installed on a vehicle with anautomatic transmission, not shown. The engine 3 includes an intake valve4 and an exhaust valve 7 provided for each cylinder 3 a, for opening andclosing an intake port and an exhaust port thereof, respectively, anintake camshaft 5 and intake cams 6 for actuating the intake valves 4, avariable intake valve-actuating mechanism 40 that actuates the intakevalves 4 to open and close the same, an exhaust camshaft 8 and exhaustcams 9 for actuating the exhaust valves 7, an exhaust valve-actuatingmechanism 30 that actuates the exhaust valves 7 to open and close thesame, fuel injection valves 10, spark plugs 11 (see FIG. 2), and soforth.

The intake valve 4 has a stem 4 a thereof slidably fitted in a guide 4b. The guide 4 b is rigidly fixed to a cylinder head 3 c. Further, asshown in FIG. 4, the intake valve 4 includes upper and lower springsheets 4 c and 4 d, and a valve spring 4 e disposed therebetween, andthe stem 4 a is urged by the valve spring 4 e in the valve-closingdirection.

Further, the intake camshaft 5 and the exhaust camshaft 8 are rotatablymounted through the cylinder head 3 c via holders, not shown. The intakecamshaft 5 has an intake sprocket (not shown) coaxially and rotatablyfitted on one end thereof. The intake sprocket is connected to acrankshaft 3 d via a timing chain, not shown, and connected to theintake camshaft 5 via a variable cam phase mechanism 70, describedhereinafter. With the above arrangement, the intake camshaft 5 performsone rotation per two rotations of the crankshaft 3 d. Further, theintake cam 6 is provided on the intake camshaft 5 for each cylinder 3 asuch that the intake cam 6 rotates in unison with the intake camshaft 5.

Furthermore, the variable intake valve-actuating mechanism 40 isprovided for actuating the intake valve 4 of each cylinder 3 a so as toopen and close the same, in accordance with rotation of the intakecamshaft 5, and continuously changing the lift and the valve timing ofthe intake valve 4, which will be described in detail hereinafter. Itshould be noted that in the present embodiment, “the lift of the intakevalve 4” (hereinafter referred to as “the valve lift”). represents themaximum lift of the intake valve 4.

On the other hand, the exhaust valve 7 has a stem 7 a thereof slidablyfitted in a guide 7 b. The guide 7 b is rigidly fixed to the cylinderhead 3 c. Further, the exhaust valve 7 includes upper and lower springsheets 7 c and 7 d, and a valve spring 7 e disposed therebetween, andthe stem 7 a is urged by the valve spring 7 e in the valve-closingdirection.

Further, the exhaust camshaft 8 has an exhaust sprocket (not shown)integrally formed therewith, and is connected to the crankshaft 3 d bythe exhaust sprocket and the timing chain, not shown, whereby theexhaust camshaft 8 performs one rotation per two rotations of thecrankshaft 3 d. Further, the exhaust cam 9 is provided on the exhaustcamshaft 8 for each cylinder 3 a such that the exhaust cam 9 rotates inunison with the exhaust camshaft 8.

Further, the exhaust valve-actuating mechanism 30 includes rocker arms31. Each rocker arm 31 is pivotally moved in accordance with rotation ofthe associated exhaust cam 9 to thereby actuate the exhaust valve 7 foropening and closing the same against the urging force of the valvespring 7 e.

On the other hand, the fuel injection valve 10 is provided for eachcylinder 3 a, and mounted through the cylinder head 3 c in a tiltedstate such that fuel is directly injected into a combustion chamber.That is, the engine 3 is configured as a direct injection engine.Further, the fuel injection valve 10 is electrically connected to theECU 2 and the valve-opening time period and the valve-opening timingthereof are controlled by the ECU 2, whereby the fuel injection amountis controlled.

The spark plug 11 as well is provided for each cylinder 3 a, and mountedthrough the cylinder head 3 c. The spark plug 11 is electricallyconnected to the ECU 2, and a state of spark discharge is controlled bythe ECU 2 such that a mixture in the combustion chamber is burned intiming corresponding to ignition timing.

On the other hand, the engine 3 is provided with a crank angle sensor 20and an engine coolant temperature sensor 21. The crank angle sensor 20is comprised of a magnet rotor and an MRE (magnetic resistance element)pickup, and delivers a CRK signal and a TDC signal, which are both pulsesignals, to the ECU 2 in accordance with rotation of the crankshaft 3 d.Each pulse of the CRK signal is generated whenever the crankshaft 3 drotates through a predetermined angle (e.g. 1°). The ECU 2 calculatesthe rotational speed NE of the engine 3 (hereinafter referred to as “theengine speed NE”) based on the CRK signal. It should be noted that inthe present embodiment, the crank angle sensor 20 corresponds toreference parameter-detecting means, and the engine speed NE to areference parameter. The TDC signal indicates that the piston 3 b hascome to a predetermined crank angle position immediately before the TDCposition at the start of the intake stroke, on a cylinder-by-cylinderbasis, and each pulse thereof is generated whenever the crankshaft 3 drotates through a predetermined crank angle.

The engine coolant temperature sensor 21 is implemented e.g. by athermistor, and detects an engine coolant temperature TW to deliver asignal indicative of the sensed engine coolant temperature TW to the ECU2. The engine coolant temperature TW is the temperature of an enginecoolant circulating through a cylinder block 3 h of the engine 3.

Further, the engine 3 has an intake pipe 12 from which a throttle valvemechanism is omitted, and an intake passage 12 a having a large diameteris formed through the intake pipe 12, whereby the engine 3 is configuredsuch that flow resistance is smaller than in an ordinary engine. Theintake pipe 12 is provided with an air flow sensor 22 and an intake airtemperature sensor 23 (see FIG. 2).

The air flow sensor 22 is implemented by a hot-wire air flow meter, anddetects the flow rate Gin of air (hereinafter referred to as “the airflow rate Gin”) flowing through the intake passage 12 a to deliver asignal indicative of the sensed air flow rate Gin to the ECU 2. Itshould be noted that the air flow rate Gin is indicated in units ofg/sec. Further, the intake air temperature sensor 23 detects thetemperature TA of intake air (hereinafter referred to as “the intake airtemperature TA”) flowing through the intake passage 12 a, and delivers asignal indicative of the sensed intake air temperature TA to the ECU 2.

Further, a LAF sensor 24 and a catalytic device 14 are provided in theexhaust pipe 13 at respective locations in the mentioned order from theupstream side. The LAF sensor 24 is comprised of a zirconia layer andplatinum electrodes, and linearly detects the concentration of oxygen inexhaust gases flowing through an exhaust passage 13 a of the exhaustpipe 13, in a broad air-fuel ratio range from a rich region richer thana stoichiometric air-fuel ratio to a very lean region, and delivers asignal indicative of the sensed oxygen concentration to the ECU 2.

The ECU 2 calculates an actual air-fuel ratio KACT indicative of theair-fuel ratio in exhaust gases, based on the value of the signal fromthe LAF sensor 24. In this case, the actual air-fuel ratio KACT iscalculated as an equivalent ratio. It should be noted that in thepresent embodiment, the LAF sensor 24 corresponds to controlledvariable-detecting means, and the actual air-fuel ratio KACT to acontrolled variable and the air-fuel ratio of the mixture.

Next, a description will be given of the aforementioned variable intakevalve-actuating mechanism 40. As shown in FIG. 4, the variable intakevalve-actuating mechanism 40 is comprised of the intake camshaft 5, theintake cams 6, a variable valve lift mechanism 50, and the variable camphase mechanism 70.

The variable valve lift mechanism 50 actuates the intake valves 4 toopen and close the same, in accordance with rotation of the intakecamshaft 5, and continuously changes the valve lift Liftin between apredetermined maximum value Liftinmax and 0. The variable valve liftmechanism 50 is comprised of rocker arm mechanisms 51 of a four jointlink type, provided for the respective cylinders 3 a, and a liftactuator 60 (see FIGS. 5A and 5B) simultaneously actuating these rockerarm mechanisms 51. It should be noted that in the present embodiment,the variable valve lift mechanism 50 corresponds to a variable intakemechanism.

Each rocker arm mechanism 51 is comprised of a rocker arm 52, and upperand lower links 53 and 54. The upper link 53 has one end pivotallymounted to an upper end of the rocker arm 52 by an upper pin 55, and theother end pivotally mounted to a rocker arm shaft 56. The rocker armshaft 56 is mounted through the cylinder head 3 c via holders, notshown.

Further, a roller 57 is pivotally disposed on the upper pin 55 of therocker arm 52. The roller 57 is in contact with a cam surface of theintake cam 6. As the intake cam 6 rotates, the roller 57 rolls on theintake cam 6 while being guided by the cam surface of the intake cam 6.As a result, the rocker arm 52 is vertically driven, and the upper link53 is pivotally moved about the rocker arm shaft 56.

Furthermore, an adjusting bolt 52 a is mounted to an end of the rockerarm 52 toward the intake valve 4. When the rocker arm 52 is verticallymoved in accordance with rotation of the intake cam 6, the adjustingbolt 52 a vertically drives the stem 4 a to open and close the intakevalve 4, against the urging force of the valve spring 4 e.

Further, the lower link 54 has one end pivotally mounted to a lower endof the rocker arm 52 by a lower pin 58, and the other end of the lowerlink 54 has a connection shaft 59 pivotally mounted thereto. The lowerlink 54 is connected to a short arm 65, described hereinafter, of thelift actuator 60 by the connection shaft 59.

On the other hand, as shown in FIGS. 5A and 5B, the lift actuator 60 iscomprised of a motor 61, a nut 62, a link 63, a long arm 64, and theshort arm 65. The motor 61 is connected to the ECU 2, and disposedoutside a head cover 3 g of the engine 3. The rotary shaft of the motor61 is a screw shaft 61 a formed with a male screw and the nut 62 isscrewed onto the screw shaft 61 a. The nut 62 is connected to the longarm 64 by the link 63. The link 63 has one end pivotally mounted to thenut 62 by a pin 63 a, and the other end pivotally mounted to one end ofthe long arm 64 by a pin 63 b.

Further, the other end of the long arm 64 is attached to one end of theshort arm 65 by a pivot shaft 66. The pivot shaft 66 is circular incross section, and extends through the head cover 3 g of the engine 3such that it is pivotally supported by the head cover 3 g. The long arm64 and the short arm 65 are pivotally moved in unison with the pivotshaft 66 in accordance with pivotal motion of the pivot shaft 66.

Furthermore, the aforementioned connection shaft 59 rotatably extendsthrough the other end of the short arm 65, whereby the short arm 65 isconnected to the lower link 54 by the connection shaft 59.

Next, a description will be given of the operation of the variable valvelift mechanism 50 configured as above. In the variable valve liftmechanism 50, when a lift control input U_Liftin, described hereinafter,is input from the ECU 2 to the lift actuator 60, the screw shaft 61 arotates, and the nut 62 is moved in accordance with the rotation of thescrew shaft 61 a, whereby the long arm 64 and the short arm 65 arepivotally moved about the pivot shaft 66, and in accordance with thepivotal motion of the short arm 65, the lower link 54 of the rocker armmechanism 51 is pivotally moved about the lower pin 58. That is, thelower link 54 is driven by the lift actuator 60.

During the above process, under the control of the ECU 2, the range ofpivotal motion of the short arm 65 is restricted between the maximumlift position shown in FIG. 5A and the zero lift position shown in FIG.5B, whereby the range of pivotal motion of the lower link 54 is alsorestricted between the maximum lift position indicated by the solid linein FIG. 4 and the zero lift position indicated by the two-dot chain linein FIG. 4.

The four joint link formed by the rocker arm shaft 56, the upper andlower pins 55 and 58, and the connection shaft 59 is configured suchthat when the lower link 54 is in the maximum lift position, thedistance between the center of the upper pin 55 and the center of thelower pin 58 becomes longer than the distance between the center of therocker arm shaft 56 and the center of the connection shaft 59, wherebyas shown in FIG. 6A, when the intake cam 6 rotates, the amount ofmovement of the adjusting bolt 52 a becomes larger than the amount ofmovement of a contact point where the intake cam 6 and the roller 57 arein contact with each other.

On the other hand, the four joint link is configured such that when thelower link 54 is in the zero lift position, the distance between thecenter of the upper pin 55 and the center of the lower pin 58 becomesshorter than the distance between the center of the rocker arm shaft 56and the center of the connection shaft 59, whereby as shown in FIG. 6B,the adjusting bolt 52 a is placed in a state substantially immovablewhen the intake cam 6 rotates.

For the above reason, during rotation of the intake cam 6, when thelower link 54 is in the maximum lift position, the intake valve 4 isopened according to a valve lift curve indicated by a solid line in FIG.7, and the valve lift Liftin takes its maximum value Liftinmax. On theother hand, when the lower link 54 is in the zero lift position, asindicated by a two-dot chain line in FIG. 7, the intake valve 4 is heldin the closed state, and the valve lift Liftin is held at 0.

Therefore, in the variable valve lift mechanism 50, the lower link 54 ispivotally moved by the lift actuator 60 between the maximum liftposition and the zero lift position, whereby it is possible tocontinuously change the valve lift Liftin between the maximum valueLiftinmax and 0.

It should be noted that the variable valve lift mechanism 50 includes alock mechanism, not shown, and the lock mechanism locks the operation ofthe variable valve lift mechanism 50 when the lift control inputU_Liftin is set to a failure-time value U_Liftin_fs, as describedhereinafter, or when the lift control input U_Liftin is not input fromthe ECU 2 to the lift actuator 60 e.g. due to a disconnection. That is,the variable valve lift mechanism 50 is inhibited from changing thevalve lift Liftin, whereby the valve lift Liftin is held at apredetermined locked value. It should be noted that when a cam phaseCain is held at a locked value, described hereinafter, the predeterminedlocked value is set to such a value as will make it possible to ensure apredetermined failure-time value Gcyl_fs of the intake air amount,described hereinafter. The predetermined failure-time value Gcyl_fs isset to a value which is capable of suitably carrying out idling orstarting of the engine 3 during stoppage of the vehicle, and capable ofmaintaining a low-speed traveling state of the vehicle during travel ofthe vehicle.

The engine 3 is provided with a pivot angle sensor 25 (see FIG. 2). Thepivot angle sensor 25 detects a pivot angle of the pivot shaft 66, i.e.the short arm 65, and delivers a signal indicative of the detected pivotangle of the short arm 65 to the ECU 2. The ECU 2 calculates the valvelift Liftin based on the detection signal from the pivot angle sensor25. It should be noted that in the present embodiment, the pivot anglesensor 25 corresponds to reference parameter-detecting means, and thevalve lift Liftin to a reference parameter and an operating stateparameter.

Next, a description will be given of the aforementioned variable camphase mechanism 70. The variable cam phase mechanism 70 is provided forcontinuously advancing or retarding the relative phase Cain of theintake camshaft 5 with respect to the crankshaft 3 d (hereinafterreferred to as “the cam phase Cain”), and mounted on an intakesprocket-side end of the intake camshaft 5. As shown in FIG. 8, thevariable cam phase mechanism 70 includes a housing 71, a three-bladedvane 72, an oil pressure pump 73, and a solenoid valve mechanism 74.

The housing 71 is integrally formed with the intake sprocket on theintake camshaft 5 d, and divided by three partition walls 71 a formed atequal intervals. The vane 72 is coaxially mounted on the end of theintake camshaft 5 where the intake sprocket is mounted, such that theblades of the vane 72 radially extends outward from the intake camshaft5, and are rotatably housed in the housing 71. Further, the housing 71has three advance chambers 75 and three retard chambers 76 each formedbetween one of the partition walls 71 a and one of the three blades ofthe vane 72.

The oil pressure pump 73 is a mechanically-driven type which isconnected to the crankshaft 3 d. As the crankshaft 3 d rotates, the oilpressure pump 73 draws lubricating oil stored in an oil pan 3 e of theengine 3 via a lower part of an oil passage 77 c, for pressurization,and supplies the pressurized oil to the solenoid valve mechanism 74 viathe remaining part of the oil passage 77 c.

The solenoid valve mechanism 74 is formed by combining a spool valvemechanism 74 a and a solenoid 74 b, and is connected to the advancechambers 75 and the retard chambers 76 via an advance oil passage 77 aand a retard oil passage 77 b such that oil pressure supplied from theoil pressure pump 73 is delivered to the advance chambers 75 and theretard chambers 76 as advance oil pressure Pad and retard oil pressurePrt, respectively. The solenoid 74 b of the solenoid valve mechanism 74is electrically connected to the ECU 2. When a phase control inputU_Cain, described hereinafter, is input from the ECU 2, the solenoid 74b moves a spool valve element of the spool valve mechanism 74 a within apredetermined range of motion according to the phase control inputU_Cain to thereby change both the advance oil pressure Pad and theretard oil pressure Prt.

In the variable cam phase mechanism 70 configured as above, duringoperation of the oil pressure pump 73, the solenoid valve mechanism 74is operated according to the phase control input U_Cain, to supply theadvance oil pressure Pad to the advance chambers 75 and the retard oilpressure Prt to the retard chambers 76, whereby the relative phase ofthe vane 72 with respect to the housing 71 is changed toward an advancedside or a retarded side. As a result, the cam phase Cain described aboveis continuously changed between a most retarded value Cainrt (valuecorresponding to a cam angle of e.g. 0°) and a most advanced valueCainad (value corresponding to a cam angle of e.g. 55°), whereby thevalve timing of the intake valves 4 is continuously changed between mostretarded timing indicated by a solid line in FIG. 9 and most advancedtiming indicated by a two-dot chain line in FIG. 9.

It should be noted that the variable cam phase mechanism 70 includes alock mechanism, not shown, which locks the operation of the variable camphase mechanism 70, when oil pressure supplied from the oil pressurepump 73 is low, when the phase control input U_Cain is set to afailure-time value U_Cain_fs, described hereinafter, or when the phasecontrol input U_Cain is not input to the solenoid valve mechanism 74e.g. due to a disconnection. That is, the variable cam phase mechanism70 is inhibited from changing the cam phase Cain, whereby the cam phaseCain is held at the predetermined locked value. The predetermined lockedvalue is set to such a value as will make it possible to ensure thepredetermined failure-time value Gcyl_fs of the intake air amount whenthe valve lift Liftin is held at the predetermined locked value, asdescribed above.

As described above, in the variable intake valve-actuating mechanism 40of the present embodiment, the variable valve lift mechanism 50continuously changes the valve lift Liftin between the maximum valueLiftinmax thereof and 0, and the variable cam phase mechanism 70continuously changes the cam phase Cain, i.e. the valve timing of theintake valves 4 between the most retarded timing and the most advancedtiming, described hereinbefore. Further, as described hereinafter, theECU 2 controls the valve lift Liftin and the cam phase Cain via thevariable valve lift mechanism 50 and the variable cam phase mechanism70, whereby the intake air amount is controlled.

On the other hand, a cam angle sensor 26 (see FIG. 2) is disposed at anend of the intake camshaft 5 opposite from the variable cam phasemechanism 70. The cam angle sensor 26 is implemented e.g. by a magnetrotor and an MRE pickup, for delivering a CAM signal, which is a pulsesignal, to the ECU 2 along with rotation of the intake camshaft 5. Eachpulse of the CAM signal is generated whenever the intake camshaft 5rotates through a predetermined cam angle (e.g. 1°). The ECU 2calculates the cam phase Cain based on the CAM signal and the CRKsignal, described above.

Next, as shown in FIG. 2, connected to the ECU 2 are an acceleratorpedal opening sensor 27, and an ignition switch (hereinafter referred toas “the IG·SW”) 28. The accelerator pedal opening sensor 27 detects astepped-on amount AP of an accelerator pedal, not shown, of the vehicle(hereinafter referred to as “the accelerator pedal opening AP”) anddelivers a signal indicative of the sensed accelerator pedal opening APto the ECU 2. Further, the IG·SW 28 is turned on or off by operation ofan ignition key, not shown, and delivers a signal indicative of theON/OFF state thereof to the ECU 2.

The ECU 2 is implemented by a microcomputer comprised of a CPU, a RAM, aROM and an I/O interface (none of which are specifically shown). The ECU2 determines operating conditions of the engine 3, based on the signalsfrom the aforementioned sensors 20 to 27 and the ON/OFF signal from theIG·SW 28, and executes the control processes. More specifically, the ECU2 executes air-fuel ratio control and ignition timing control, accordingto the operating conditions of the engine 3, as described hereinafter.In addition, the ECU 2 calculates a corrected valve lift Liftin_mod, andcontrols the valve lift Liftin and the cam phase Cain via the variablevalve lift mechanism 50 and the variable cam phase mechanism 70, tothereby control the intake air amount.

It should be noted that in the present embodiment, the ECU 2 correspondsto the controlled variable-detecting means, the referenceparameter-detecting means, target controlled variable-setting means,control input-calculating means, error parameter-calculating means,model-modifying means, and first input value-calculating means.

Next, a description will be given of the control apparatus 1 accordingto the present embodiment. The control apparatus 1, as shown in FIG. 10,includes an air-fuel ratio controller 100 which performs the air-fuelratio control. As will be described hereinafter, the air-fuel ratiocontroller 100 is provided for calculating the fuel injection amountTOUT for each fuel injection valve 10, and implemented by the ECU 2. Itshould be noted that in the present embodiment, the air-fuel ratiocontroller 100 corresponds to the control input-calculating means, andthe fuel injection amount TOUT to a control input and the amount of fuelto be supplied to the engine.

The air-fuel ratio controller 100 includes first and second estimatedintake air amount-calculating sections 101 and 102, a transitioncoefficient-calculating section 103, amplification elements 104 and 105,an addition element 106, an amplification element 107, a target air-fuelratio-calculating section 108, an air-fuel ratio correctioncoefficient-calculating section 109, a total correctioncoefficient-calculating section 110, a multiplication element 111, afuel attachment-dependent correction section 112, an air-fuel ratioerror estimated value-calculating section 113, an addition element 114,and a lift correction value-calculating section 120.

First, as described hereinafter, the first estimated intake airamount-calculating section 101 calculates a first estimated intake airamount Gcyl_vt. It should be noted that in the present embodiment, thefirst estimated intake air amount-calculating section 101 corresponds toa first input value-calculating section, and the first estimated intakeair amount Gcyl_vt corresponds to a first input value.

First, the first estimated intake air amount-calculating section 101calculates a basic estimated intake air amount Gcyl_vt_base by searchinga map shown in FIG. 11, according to the engine speed NE and thecorrected valve lift Liftin_mod. The corrected valve lift Liftin_mod isa value obtained by correcting the valve lift Liftin using a liftcorrection value Dlift, described hereinafter. The reason for using thecorrected valve lift Liftin_mod for calculating the first estimatedintake air amount Gcyl_vt will be described hereinafter. It should benoted that the first estimated intake air amount-calculating section 101uses a downsampled value as the corrected valve lift Liftin_mod.Further, in FIG. 11, NE 1 to NE3 represent predetermined values of theengine speed NE, which satisfy the relationship of NE1<NE2<NE3. Thisalso applies to the following description.

In this map, when NE=NE1 or NE2 holds, in a region where the correctedvalve lift Liftin_mod is small, the basic estimated intake air amountGcyl_vt_base is set to a larger value as the corrected valve liftLiftin_mod is larger, whereas in a region where the corrected valve liftLiftin_mod is close to the maximum value Liftinmax, the basic estimatedintake air amount Gcyl_vt_base is set to a smaller value as thecorrected valve lift Liftin_mod is larger. This is because in alow-to-medium engine speed region, as the corrected valve liftLiftin_mod is larger in the region where the corrected valve liftLiftin_mod is close to the maximum value Liftinmax, the valve-openingtime period of the intake valve 4 becomes longer, whereby chargingefficiency is reduced by blow-back of intake air. Further, when NE=NE3holds, the basic estimated intake air amount Gcyl_vt_base is set to alarger value as the corrected valve lift Liftin_mod is larger. This isbecause in a high engine speed region, the above-described blow-back ofintake air is made difficult to occur even in a region where thecorrected valve lift Liftin_mod is large, due to the inertia force ofintake air, so that the charging efficiency becomes higher as thecorrected valve lift Liftin_mod is larger.

Further, a correction coefficient K_gcyl_vt is calculated by searching amap shown in FIG. 12, according to the engine speed NE and the cam phaseCain. In this map, when NE=NE1 or NE2 holds, in a region where the camphase Cain is close to the most retarded value Cainrt, the correctioncoefficient K_gcyl_vt is set to a smaller value as the cam phase Cain iscloser to the most retarded value Cainrt, and in the other regions, thecorrection coefficient K_gcyl_vt is set to a smaller value as the camphase Cain takes a value closer to the most advanced value Cainad. Thisis because in the low-to-medium engine speed region, as the cam phaseCain is closer to the most retarded value Cainrt in the region where thecam phase Cain is close to the most retarded value Cainrt, thevalve-closing timing of the intake valve 4 is retarded, whereby thecharging efficiency is degraded by the blow-back of intake air, and inthe other regions, as the cam phase Cain takes a value closer to themost advanced value Cainad, the valve overlap increases to increase theinternal EGR amount, whereby the charging efficiency is degraded.Further, when NE=NE3 holds, in the region where the cam phase Cain isclose to the most retarded value Cainrt, the correction coefficientK_gcyl_vt is set to a fixed value (a value of 1), and in the otherregions, the correction coefficient K_gcyl_vt is set to a smaller valueas the cam phase Cain takes a value closer to the most advanced valueCainad. This is because in the high engine speed region, the blow-backof intake air is made difficult to occur even in a region where the camphase Cain is close to the most advanced value Cainad, due to theabove-mentioned inertia force of intake air.

Then, the first estimated intake air amount Gcyl_vt is calculated usingthe basic estimated intake air amount Gcyl_vt_base and the correctioncoefficient K_gcyl_vt, calculated as above, by the following equation(1):Gcyl _(—) vt(n)=K _(—) gcyl _(—) vt(n)·Gcyl _(—) vt_base(n)  (1)

In the above equation (1), discrete data with a symbol (n) indicatesthat it is data sampled or calculated at a control period ΔTnsynchronous with generation of each TDC signal pulse. The symbol nindicates a position in the sequence of sampling or calculating cyclesof respective discrete data. For example, the symbol n indicates thatdiscrete data therewith is a value sampled in the current controltiming, and a symbol n−1 indicates that discrete data therewith is avalue sampled in the immediately preceding control timing. It should benoted that in the following description, the symbol (n) and the likeprovided for the discrete data are omitted as deemed appropriate.

Now, the method of calculating the first estimated intake air amountGcyl_vt in the first estimated intake air amount-calculating section 101is not limited to the above-described method, but any suitable methodmay be employed insofar as it calculates the first estimated intake airamount Gcyl_vt according to the engine speed NE, the corrected valvelift Liftin_mod, and the cam phase Cain. For example, the firstestimated intake air amount Gcyl_vt may be calculated using a4-dimensional map in which the relationship between the first estimatedintake air amount Gcyl_vt, the engine speed NE, the corrected valve liftLiftin_mod, and the cam phase Cain is set in advance. Further, the firstestimated intake air amount Gcyl_vt may be calculated using a neuralnetwork to which are input the engine speed NE, the corrected valve liftLiftin_mod, and the cam phase Cain, and from which is output the firstestimated intake air amount Gcyl_vt.

Further, the transition coefficient-calculating section 103 calculates atransition coefficient Kg as follows: First, an estimated flow rateGin_vt (in units of g/sec) is calculated by the following equation (2),using the first estimated intake air amount Gcyl_vt calculated by thefirst estimated intake air amount-calculating sections 101, and theengine speed NE.

$\begin{matrix}{{{Gin\_ vt}(n)} = \frac{{2 \cdot {Gcyl\_ vt}}{(n) \cdot {{NE}(n)}}}{60}} & (2)\end{matrix}$

Subsequently, the transition coefficient Kg is calculated by searching atable shown in FIG. 13 according to the estimated flow rate Gin_vt. InFIG. 13, Gin1 and Gin2 represent predetermined values which satisfy therelationship of Gin1<Gin2. Since the flow rate of air flowing throughthe intake passage 12 a is small when the estimated flow rate Gin_vt iswithin the range of the Gin_vt≦Gin1, the predetermined value Gin1 is setto such a value as will cause the reliability of the first estimatedintake air amount Gcyl_vt to exceed that of a second estimated intakeair amount Gcyl_afm, referred to hereinafter, due to the resolution ofthe air flow sensor 22. Further, since the flow rate of air flowingthrough the intake passage 12 a is large when the estimated flow rateGin_vt is within the range of Gin2≦Gin_vt, the predetermined value Gin2is set to such a value as will cause the reliability of the secondestimated intake air amount Gcyl_afm to exceed that of the firstestimated intake air amount Gcyl_vt. Furthermore, in this table, thetransition coefficient Kg is set to 0 when the first estimated intakeair amount Gcyl_vt is in the range of Gin_vt≦Gin1, and to 1 when thesame is within the range of Gin2≦Gin_vt. When the estimated flow rateGin_vt is within the range of Gin1<Gin_vt<Gin2, the transitioncoefficient Kg is set to a value which is between 0 and 1, and at thesame time larger as the estimated flow rate Gin_vt is larger.

On the other hand, the second estimated intake air amount-calculatingsection 102 calculates the second estimated intake air amount Gcyl_afm(unit: g) based on the air flow rate Gin and the engine speed NE, by thefollowing equation (3):

$\begin{matrix}{{{Gcyl\_ afm}(n)} = \frac{{{Gin}(n)} \cdot 60}{2 \cdot {{NE}(n)}}} & (3)\end{matrix}$

The amplification elements 104 and 105 amplify the first and secondestimated intake air amounts Gcyl_vt and Gcyl_afm, calculated as above,to a (1−Kg)-fold and a Kg-fold, respectively. The addition element 106calculates a calculated intake air amount Gcyl based on the values thusamplified, by a weighted average arithmetic operation expressed by thefollowing equation (4):Gcyl(n)=Kg·Gcyl _(—) afm(n)+(1−Kg)·Gcyl _(—) vt(n)  (4)

As is clear from the equation (4), when Kg=0, i.e. within theaforementioned range of Gin_vt≦Gin1, Gcyl=Gcyl_vt holds, and when Kg=1,i.e. within the aforementioned range of Gin2≦Gin_vt, Gcyl=Gcyl_afmholds. When 0<Kg<1, i.e. when the estimated flow rate Gin_vt is withinthe range of Gin1<Gin_vt<Gin2, the degrees of contributions of (thedegrees of weighting) the first and second estimated intake air amountsGcyl_vt and Gcyl_afm in the calculated intake air amount Gcyl aredetermined by the value of the transition coefficient Kg.

Furthermore, the amplification element 107 calculates a basic fuelinjection amount Tcyl_bs based on the calculated intake air amount Gcyl,by the following equation (5). It should be noted that in the followingequation (5), Kgt represents a conversion coefficient set in advance foreach fuel injection valve 10.Tcyl _(—) bs(n)=Kgt·Gcyl(n)  (5)

Further, the target air-fuel ratio-calculating section 108 calculates atarget air-fuel ratio KCMD by searching a map shown in FIG. 14 accordingto the calculated intake air amount Gcyl and the accelerator pedalopening AP. In this map, the value of the target air-fuel ratio KCMD isset as an equivalent ratio, and basically, it is set to a value (a valueof 1.0) corresponding to a stoichiometric air-fuel ratio so as tomaintain excellent emission-reducing performance of the catalyticconverter. It should be noted that in the present embodiment, the targetair-fuel ratio-calculating section 108 corresponds to target controlledvariable-setting means, and the target air-fuel ratio KCMD correspondsto a target controlled variable.

Furthermore, the air-fuel ratio correction coefficient-calculatingsection 109 calculates an air-fuel ratio correction coefficient KAF witha sliding mode control algorithm expressed by the following equations(6) to (10). It should be noted that in the above equations (6) to (10),discrete data with a symbol (m) indicates that it is data sampled orcalculated every combustion cycle, i.e. whenever a total of foursuccessive pulses of the TDC signal are generated. The symbol mindicates a position in the sequence of sampling cycles of respectivediscrete data.KAF(m)=Urch′(m)+Uadp′(m)  (6)Urch′(m)=−Krch′·σ′(m)  (7)Uadp′(m)=Uadp′(m−1)−Kadp′·σ(m)  (8)σ′(m)=e(m)+S′·e(m−1)  (9)e(m)=KACT(m)−KCMD(m)  (10)

As shown in the equation (6), the air-fuel ratio correction coefficientKAF is calculated as the sum of a reaching law input Urch′ and anadaptive law input Uadp′ and the reaching law input Urch′ is calculatedusing the equation (7). In the equation (7), Krch′ represents apredetermined reaching law gain, and σ′ represents a switching functiondefined by the equation (9). In the equation (9), S′ represents aswitching function-setting parameter set to a value which satisfies therelationship of −1<S′<0 and the symbol e represents a follow-up errordefined by the equation (10). In this case, the convergence rate of thefollow-up error “e” to 0 is designated by a value set to the switchingfunction-setting parameter S′.

Furthermore, the adaptive law input Uadp′ is calculated by the equation(8). In the equation (8), Kadp′ represents a predetermined adaptive lawgain. It should be noted that the initial value of the adaptive lawinput Uadp′ is set to 1.

As described above, the air-fuel ratio correctioncoefficient-calculating section 109 calculates the air-fuel ratiocorrection coefficient KAF as a value for causing the actual air-fuelratio KACT to converge to the target air-fuel ratio KCMD, with thesliding mode control algorithm expressed by the following equations (6)to (10). It should be noted that in the present embodiment, the air-fuelratio correction coefficient KAF corresponds to a second input value.

On the other hand, the total correction coefficient-calculating section110 calculates various correction coefficients by searching respectiveassociated maps, not shown, according to parameters, such as the enginecoolant temperature TW and the intake air temperature TA, indicative ofthe operating conditions of the engine, and calculates a totalcorrection coefficient KTOTAL by multiplying the thus calculatedcorrection coefficients by each other.

Further, the multiplication element 111 calculates a demanded fuelinjection amount Tcyl by the following equation (11):Tcyl(n)=Tcyl _(—) bs(n)·KAF(n)·KTOTAL(n)  (11)

Furthermore, the fuel attachment-dependent correction section 112calculates the fuel injection amount TOUT by performing a predeterminedfuel attachment-dependent correction process on the demanded fuelinjection amount Tcyl calculated as above. Then, the fuel injectionvalve 10 is controlled such that the fuel injection timing and thevalve-opening time period thereof are determined based on the fuelinjection amount TOUT.

Next, a description will be given of the air-fuel ratio error estimatedvalue-calculating section 113. As described hereinafter, the air-fuelratio error estimated value-calculating section 113 calculates anair-fuel ratio error estimated value Eaf. It should be noted that in thepresent embodiment, the air-fuel ratio error estimated value-calculatingsection 113 corresponds to error parameter-calculating means, theair-fuel ratio error estimated value Eaf to an error parameter and alsoto the difference between the error parameter and a predetermined targetvalue, and a value of 0 to the predetermined target value.

First, the air-fuel ratio error estimated value-calculating section 113calculates an actual air-fuel ratio estimated value KACT_hat based onthe air-fuel ratio correction coefficient KAF and the actual air-fuelratio KACT, by the following equation (12), and then calculates theair-fuel ratio error estimated value Eaf by the following equation (13).

$\begin{matrix}{{{KACT\_ hat}(k)} = \frac{{KACT}(k)}{{KAF}\left( {k - d} \right)}} & (12) \\{{{Eaf}(k)} = {{{KACT\_ hat}(k)} - {{KCMD}\left( {k - d} \right)}}} & (13)\end{matrix}$

In the above equations (12) and (13), discrete data with a symbol (k)indicates that it is data sampled or calculated at a predeterminedcontrol period ΔTk (5 msec, in the present embodiment). The symbol kindicates a position in the sequence of sampling or calculating cyclesof respective discrete data. It should be noted that in the followingdescription, the symbol (k) provided for the discrete data is omitted asdeemed appropriate. Further, in the above equations (12) and (13), asymbol “d” represents a dead time it takes for combustion gases to reachthe LAF sensor 24 from the combustion chamber.

As shown in the equation (12), the actual air-fuel ratio estimated valueKACT_hat is calculated by dividing an actual air-fuel ratio KACT(k)obtained in the current control timing by an air-fuel ratio correctioncoefficient KAF(k−d) calculated in control timing the dead time dearlier, and hence as a value which is not adversely affected by theair-fuel ratio correction coefficient KAF(k−d). More specifically, theactual air-fuel ratio estimated value KACT_hat is calculated as a valueof the actual air-fuel ratio in the current control timing, estimatedassuming that air-fuel ratio feedback control was not executed in thecontrol timing the dead time d earlier.

Therefore, the air-fuel ratio error estimated value Eaf is calculated asthe difference between the actual air-fuel ratio estimated valueKACT_hat(k) calculated as above and a target air-fuel ratio KCMD(k−d)calculated in control timing the dead time d earlier, and hence theair-fuel ratio error estimated value Eaf corresponds to an error ofair-fuel ratio control in the current control timing, estimated assumingthat the air-fuel ratio feedback control was not executed in the controltiming the dead time d earlier.

Next, a description will be given of the aforementioned lift correctionvalue-calculating section 120. The lift correction value-calculatingsection 120 calculates a lift correction value Dlift by a method,described hereinafter. It should be noted that in the presentembodiment, the lift correction value-calculating section 120corresponds to model-modifying means. As described hereinbefore, in thecontrol apparatus 1, the basic estimated intake air amount Gcyl_vt_baseis calculated using the corrected valve lift Liftin_mod obtained bycorrecting the valve lift Liftin by the lift correction value Dlift, andthe FIG. 11 map. Hereinafter, the reason for using the corrected valvelift Liftin_mod will be described.

When the intake air amount is controlled via the variable valve liftmechanism 50 as in the control apparatus 1 of the present embodiment,the correlation between the basic estimated intake air amountGcyl_vt_base (i.e. the intake air amount), the valve lift Liftin, andthe engine speed NE is basically as illustrated in a map in FIG. 15.However, when the basic estimated intake air amount Gcyl_vt_base iscalculated using such a map, there is a possibility that the mapdeviates from the actual correlation therebetween, so that thecalculated value of the basic estimated intake air amount Gcyl_vt_basecan be different from the actual value thereof.

More specifically, when the mounted state of the pivot angle sensor 25is changed e.g. by impact, or the characteristic of the pivot anglesensor 25 changes with a change in the temperature thereof, thecalculated value of the valve lift Liftin sometimes deviates from theactual value thereof, and in such a case, there occurs an error in thecalculation of the aforementioned basic estimated intake air amountGcyl_vt_base. Further, also when the dynamic characteristics of thevariable valve lift mechanism 50 (i.e. the relationship of the valvelift Liftin to the lift control input U_Liftin) are changed by wear ofcomponents of the variable valve lift mechanism 50, attachment of stain,and play produced by aging, there occurs an error in the calculation ofthe basic estimated intake air amount Gcyl_vt_base. In the followingdescription, a state where the relationship between the valve liftLiftin and the basic estimated intake air amount Gcyl_vt_base hasdeviated from the actual relationship therebetween is referred to as“the lift error”.

It is considered that the state where the above lift error occursincludes those shown in FIGS. 16 and 17. FIGS. 16 and 17 illustrateexamples in which the engine speed NE=NE1 holds. FIG. 16 shows a statein which the above-described lift error has occurred due to the offset(zero-point deviation) of the calculated value of the valve lift Liftinwith respect to the actual value thereof. Further, FIG. 17 shows a statein which the lift error has occurred due to the aforementioned change inthe dynamic characteristics of the variable valve lift mechanism 50,although there is no error between the calculated value of the valvelift Liftin and the actual value thereof. In FIGS. 16 and 17, curvesindicated by solid lines indicate states in which the lift error occursin the relationship between the valve lift Liftin and the basicestimated intake air amount Gcyl_vt_base, and curves indicated by brokenlines show states in which the lift error occurs.

As is clear from FIGS. 16 and 17, the lift error becomes larger when thevalve lift Liftin is equal to a predetermined value Liftin_a in a smalllift region than when the valve lift Liftin is equal to a predeterminedvalue Liftin_b in a large lift region. More specifically, it isunderstood that the lift error becomes larger in the small lift regionthan in the large lift region both when the lift error occurs due to theabove-described offset of the valve lift Liftin and when it occurs dueto the dynamic characteristics of the variable valve lift mechanism 50.

Further, as is clear from FIG. 18, when a change amount ΔGcyl of thebasic estimated intake air amount Gcyl_vt_base with respect to a changeamount ΔLiftin of the valve lift Liftin is considered, a value ΔGcyl_athereof in the small lift region is larger than a value ΔGcyl_b thereofin the large lift region, so that a ratio ΔGcyl/ΔLiftin between the twochange amounts satisfies the relationship of(ΔGcyl_a/ΔLiftin)>>(ΔGcyl_b/ΔLiftin).

Now, assuming that the air-fuel ratio error estimated value Eaf isgenerated due to the lift error, the degree of influence of the lifterror on the air-fuel ratio error estimated value Eaf, that is, thesensitivity of the air-fuel ratio error estimated value Eaf to the lifterror can be considered to increase or decrease in the same manner asthe magnitude of the above-described ratio ΔGcyl/ΔLiftin. In otherwords, when the air-fuel ratio error estimated value Eaf is generated,it can be considered that the probability of the air-fuel ratio errorestimated value Eaf being caused by the lift error is higher as theratio ΔGcyl/ΔLiftin is larger. Furthermore, the value of the ratioΔGcyl/ΔLiftin changes not only according to the valve lift Liftin andthe engine speed NE (see FIG. 11, referred to hereinabove) but alsoaccording to the cam phase Cain, and hence the sensitivity of theair-fuel ratio error estimated value Eaf to the lift error also changesaccording to the three values of Liftin, Ne, and Cain.

For the above reason, the lift correction value-calculating section 120calculates the lift correction value Dlift for correcting the valve liftLiftin by a method, described hereinafter, as a value whichappropriately reflects the above-described sensitivity of the air-fuelratio error estimated value Eaf to the lift error, and at the same timea change in the sensitivity of the air-fuel ratio error estimated valueEaf to the lift error, which is dependent on the engine speed NE.

As shown in FIG. 19, the lift correction value-calculating section 120is comprised of a link weight function-calculating section 121, an errorweight-calculating section 122, a transition coefficientweight-calculating section 123, a modified error-calculating section124, a basic local correction value-calculating section 125, acorrection sensitivity-calculating section 126, and a finalvalue-calculating section 127.

First, the link weight function-calculating section 121 calculates alink weight function Wcp_(i) according to the engine speed NE. It shouldbe noted that in the present embodiment, the link weight functionsWcp_(i) correspond to a plurality of predetermined functions. Here, thesubscript i (i=1 to r) of the link weight function Wcp_(i) representseach of r (r is an integer not smaller than 2) areas, describedhereinafter, of the engine speed NE, and r is set to 4 (r=4) in thepresent embodiment. The link weight function Wcp_(i) is calculated as avector which is composed of the elements of four values. Morespecifically, the link weight function Wcp_(i) is calculated bysearching a map shown in FIG. 20 according to the engine speed NE. InFIG. 20, NE×1 to NE×8 represent predetermined values of the engine speedNE, and are set such that they satisfy the relationship ofNE×1<NE×2<NE×3<NE×4<NE×5<NE×6<NE×7<NE×8. This also applies to thefollowing description.

As shown in FIG. 20, when a region within which the engine speed NE isvariable is divided into four regions of 0≦NE<NE×3, NE×1<NE<NE×5,NE×3<NE<NE×7, and NE×5<NE≦NE×8, the four link weight functions Wcp_(i)are set such that they are associated with the above four regions,respectively, and are set to positive values not larger than 1 in theregions associated therewith, whereas in regions other than theassociated regions, they are set to 0.

More specifically, the link weight function Wcp₁ is set, in a regionassociated therewith (0≦NE<NE×3), to a maximum value of 1 when NE≦NE×1holds and to a smaller positive value as the engine speed NE is higher,while in the other regions, it is set to 0. Further, the link weightfunction Wcp₂ is set, in a region associated therewith (NE×1<NE<NE×5),to a maximum value of 1 when NE=NE×3 holds and to such a value aschanges along the inclined equal sides of an isosceles triangle, whilein the other regions, it is set to 0.

Furthermore, the link weight function Wcp₃ is set, in a regionassociated therewith (NE×3<NE<NE×7), to a maximum value of 1 whenNE=NE×5 holds and to such a value as changes along the inclined equalsides of an isosceles triangle, while in the other regions, it is set to0. On the other hand, the link weight function Wcp₄ is set, in a regionassociated therewith (NE×5<NE≦NE×8), to a maximum value of 1 whenNE×7≦NE holds and to a larger positive value as the engine speed NE ishigher, while in the other regions, it is set to 0.

Moreover, the regions with which the respective four link weightfunctions Wcp_(i) are associated are set such that adjacent ones thereofoverlap each other, as described above, and the sum of the values of thelink weight functions Wcp_(i) associated with the respective overlappingregions becomes equal to the maximum value of 1 of each link weightfunction Wcp_(i). For example, when NE=NE×2 holds, the values of the twolink weight functions Wcp₁ and Wcp₂ corresponding to the value NE×2 areeach set to 0.5, and hence the sum Wcp₁+Wcp₂ of the link weightfunctions becomes equal to 1 which is equal to the maximum value of eachlink weight function Wcp_(i). Further, also when NE=NE×6 holds, the sumWcp₃+Wcp₄ of the two link weight functions Wcp₃ and Wcp₄ correspondingto the predetermined value NE×2 becomes equal to 1 which is equal to themaximum value of each link weight function Wcp_(i).

It should be noted that link weight function Wcp_(i) composed of theelements of two or three values or five or more values may be used inplace of the FIG. 20 link weight function Wcp_(i) composed of theelements of four values. In this case, the regions of the engine speedNE are only required to be set such that they overlap each other,according to the number of the elements.

The error weight-calculating section 122 calculates an error weight W bya method described hereinafter. First, a second corrected valve liftLiftin_mod_p is calculated by the following equation (14):Liftin_mod_(—) p(k)=Liftin(k)+Dlift(k−1)  (14)

As shown in the equation (14), the second corrected valve liftLiftin_mod_p is calculated as the sum of the current value Liftin(k) ofthe valve lift and the immediately preceding value Dlift(k−1) of thelift correction value. This is because the current value Dlift(k) of thelift correction value has not been calculated yet when the secondcorrected valve lift Liftin_mod_p is calculated.

Then, the error weight-calculating section 122 calculates a basic errorweight W_base by searching a map shown in FIG. 21 according to thesecond corrected valve lift Liftin_mod_p and the engine speed NE. Thebasic error weight W_base takes a value obtained by normalizing theaforementioned ratio ΔGcyl/ΔLiftin with reference to the absolute value|ΔGcyl_x/ΔLiftin_x| of a ratio ΔGcyl_x/ΔLiftin_x obtained at apredetermined minute lift and a predetermined low engine speed, that is,a value which satisfies the equation,W_base=(ΔGcyl/ΔLiftin)÷(|ΔGcyl_x/ΔLiftin_x|). As shown by broken linesin FIG. 21, on condition that ΔGcyl/ΔLiftin<0 holds, the basic errorweight W_base is set to 0 for the reason described hereinafter.

In this map, the basic error weight W_base is set to a larger value asthe second corrected valve lift Liftin_mod_p is smaller. This is becausethe aforementioned sensitivity of the air-fuel ratio error estimatedvalue Eaf to the lift error, i.e. the ratio ΔGcyl/ΔLiftin takes a largervalue as the second corrected valve lift Liftin_mod_p is smaller.Further, in the small lift region, the basic error weight W_base is setto a smaller value as the engine speed NE is higher, whereas in theother lift regions, the basic error weight W_base is set to a largervalue as the engine speed NE is higher. The reason for this is the sameas given in the description of the FIG. 11 map (changes in the chargingefficiency and the blow-back of intake air).

Further, the error weight-calculating section 122 calculates an errorweight correction coefficient K_w by searching a map shown in FIG. 22according to the cam phase Cain and the engine speed NE. The errorweight correction coefficient K_w takes a value obtained by normalizingthe aforementioned ratio ΔGcyl/ΔLiftin with reference to the absolutevalue |ΔGcyl_rt/ΔLiftin_rt| of a ratio ΔGcyl_rt/ΔLiftin_rt obtained whenthe cam phase Cain is equal to the most retarded value, at each of thepredetermined values NE1 to NE3 of the engine speed NE, that is, a valuewhich satisfies the equation,W_base=(ΔGcyl/ΔLiftin)÷(|ΔGcyl_rt/ΔLiftin_rt |).

In this map, the error weight correction coefficient K_w is set to havethe same tendency as that of the FIG. 12 correction coefficientK_gcyl_vt described above, with respect to the engine speed NE and thecam phase Cain. The reason for this is the same as given in thedescription of the FIG. 12 map (changes in the charging efficiency andthe blow-back of intake air).

Then, finally, the error weight W is calculated by the followingequation (15).W(k)=W_base(k)·K _(—) w(k)  (15)

Thus, the error weight W is calculated by multiplying the basic errorweight W_base by the error weight correction coefficient K_w, and hencethe error weight W is calculated as a value which represents thesensitivity of the air-fuel ratio error estimated value Eaf to the lifterror. More specifically, the error weight W is calculated as a largervalue as the sensitivity of the air-fuel ratio error estimated value Eafto the lift error, i.e. the ratio ΔGcyl/ΔLiftin is larger, in otherwords, as the probability of the air-fuel ratio error estimated valueEaf being caused by the lift error is higher. Further, the two valuesW_base and K_w are calculated by searching the two maps shown in FIGS.21 and 22 according to the three parameters Liftin_mod_p, NE, and Cain,and the second corrected valve lift Liftin_mod_p is a value obtained byadding the immediately preceding value Dlift(k−1) of the lift correctionvalue to the valve lift, so that it can be considered that the above twomaps form a response surface model which represents the correlationbetween the three values Liftin, NE, and Cain, and the error weight W.

Thus, the error weight W is calculated according to the three valuesLiftin, NE, and Cain since the sensitivity of the air-fuel ratio errorestimated value Eaf to the lift error is changed not only by the valueof the valve lift Liftin but also by the values of the engine speed NEand the cam phase Cain. As a result, the error weight W is calculated asa value which represents the degree of influence of the three valuesLiftin, NE, and Cain on the air-fuel ratio error estimated value Eaf.

It should be noted that the FIG. 21 map for use in calculating the basicerror weight W_base may be replaced by a map in which the basic errorweight W_base is set according to the valve lift Liftin and the enginespeed NE, that is, a map in which the second corrected valve liftLiftin_mod_p represented by the horizontal axis in FIG. 21 is replacedby the valve lift Liftin.

The transition coefficient weight-calculating section 123 calculates atransition coefficient weight Wkg by the following equation (16):Wkg(k)=1−Kg(k−d)  (16)

In the above equation (16), a transition coefficient Kg(k−d) the deadtime d earlier is used for the following reason: As is clear fromreference to the aforementioned equation (4), when the transitioncoefficient Kg changes, the degrees of contributions of the firstestimated intake air amount Gcyl_vt and the second estimated intake airamount Gcyl_afm in the calculated intake air amount Gcyl also change tochange the sensitivity of the air-fuel ratio error estimated value Eafto the lift error. In this case, the air-fuel ratio error estimatedvalue Eaf calculated in the current control timing is caused by acalculated intake air amount Gcyl(k−d) calculated in control timing thedead time d earlier and the fuel injection amount TOUT calculated basedon the calculated intake air amount Gcyl(k−d), so that it is assumedthat the change in the sensitivity of the air-fuel ratio error estimatedvalue Eaf to the lift error in the current control timing is caused by achange in the transition coefficient Kg(k−d) the dead time d earlier.Therefore, to compensate for the change in the sensitivity of theair-fuel ratio error estimated value Eaf to the lift error, thetransition coefficient Kg(k−d) the dead time d earlier is employed forcalculation of the transition coefficient weight Wkg.

Then, the modified error-calculating section 124 calculates a totalweight Wg_(i) by the following equation (17), and calculates modifiederrors Weaf_(i) using the total weight Wg_(i) and the air-fuel ratioerror estimated value Eaf by the following equation (18).Wg _(i)(k)=Wcp _(i)(k)·W(k)·Wkg(k)  (17)Weaf _(i)(k)=Wg _(i)(k)·Eaf(k)  (18)

Thus, the modified error Weaf_(i) is calculated as a vector which iscomposed of the elements of four values. Further, since the modifiederror Weaf_(i) is calculated by multiplying the air-fuel ratio errorestimated value Eaf by the three values Wkg, W, and Wcp_(i), themodified error Weaf_(i) is calculated as a value weighted by these threevalues. It should be noted that in the present embodiment, the modifiederrors Weaf_(i) correspond to a plurality of first multiplicationvalues.

Further, the basic local correction value-calculating section 125calculates a basic local correction value Dlift_bs_(i) with a controlalgorism to which is applied a sliding mode control algorithm expressedby the following equations (19) to (26). Thus, the basic localcorrection value Dlift_bs_(i) is calculated as a vector which iscomposed of the elements of four values for causing the modified errorsWeaf_(i) to converge to 0. In other words, the basic local correctionvalues Dlift_bs_(i) are calculated such that the difference (i.e. theair-fuel ratio error estimated value Eaf) between the air-fuel ratioerror estimated value Eaf and 0 as a predetermined target value iscaused to converge to 0.σ_(i)(k)=Weaf _(i)(k)+S·Weaf _(i)(k−1)  (19)Urch _(i)(k)=−Krch·σ _(i)(k)  (20)Unl _(i)(k)=−Knl·sgn(σ_(i)(k))  (21)Uadp _(i)(k)=−Kadp·δ _(i)(k)  (22)δ_(i)(k)=λ·δ_(i)(k−1)+σ_(i)(k)  (23)When Dlift_(—) bs _(—) L<Dlift_(—) bs _(i)(k−1)<Dlift_(—) bs _(—)Hλ=1  (24)When Dlift_(—) bs _(i)(k−1)≦Dlift_(—) bs _(—) L or Dlift_(—) bs _(—)H≦Dlift_(—) bs _(i)(k−1) λ=λlmt  (25)Dlift_(—) bs _(i)(k)=Urch _(i)(k)+Unl _(i)(k)+Uadp _(i)(k)  (26)

In the above equation (19), σ_(i) represents a switching function, and Srepresents a switching function-setting parameter set to a value whichsatisfies the relationship of −1<S<0. In this case, the convergence rateof the modified errors Weaf_(i) to 0 is designated by a value set to theswitching function-setting parameter S. Further, in the equation (20),Urch_(i) represents a reaching law input, and Krch a predeterminedreaching law gain. Furthermore, in the equation (21), Unl_(i) representsa non-linear input, and Knl a predetermined non-linear input gain.Further, in the equation (21), sgn(σ_(i)(k)) represents a sign function,and the value thereof is set such that sgn(σ_(i)(k))=1 holds whenσ_(i)(k)≧−0, and when σ_(i)(k)<0, sgn(σ_(i)(k))=−1 holds (it should benoted that the value thereof may be set such that sgn(σ_(i)(k))=0 holdswhen σ_(i)(k)=0).

In the equation (22), Uadp_(i) represents an adaptive law input, andKadp represents a predetermined adaptive law gain. Further, in theequation (22), δ_(i) represents the integral value of a switchingfunction calculated by the equation (23). In the equation (23), λrepresents a forgetting coefficient, and as shown in the equations (24)and (25), the value thereof is set to 1 or a predetermined value λlmt,according to the results of comparison between the immediately precedingvalue Dlift_bs_(i)(k−1) of the basic local correction value andpredetermined upper and lower limit values Dlift_bs_H and Dlift_bs_L.The upper limit value Dlift_bs_H is set to a predetermined positivevalue, and the lower limit value Dlift_bs_L is set to a predeterminednegative value, while the predetermined value λlmt is set to a valuewhich satisfies the relationship of 0<λlmt<1.

Further, as shown in the equation (26), the basic local correction valueDlift_bs_(i) is calculated as the sum of the reaching law inputUrch_(i), the non-linear input Unl_(i), and the adaptive law inputUadp_(i). It should be noted that in the present embodiment, the basiclocal correction values Dlift_bs_(i) correspond to a plurality ofmodification values.

As described above, the basic local correction value Dlift_bs_(i) iscalculated such that the modified error Weaf_(i) weighted by the threevalues Wkg, W, and Wcp_(i) becomes equal to 0. In this case, the twovalues Wkg and W thereof are used as multiplication values by which theair-fuel ratio error estimated value Eaf is multiplied, whereby thebasic local correction value Dlift_bs_(i) are calculated as values onwhich are reflected the influence of the degree of contribution of thefirst estimated intake air amount Gcyl_vt on the air-fuel ratio errorestimated value Eaf, and the sensitivity of the air-fuel ratio errorestimated value Eaf to the lift error.

Further, since the link weight functions Wcp_(i) are used asmultiplication values by which the air-fuel ratio error estimated valueEaf is multiplied, the basic local correction values Dlift_bs_(i) arecalculated such that the air-fuel ratio error estimated value Eaf isdistributed to the aforementioned four engine speed regions, whereby thebasic local correction values Dlift_bs_(i) are calculated such that oneor two of them associated with the engine speed NE in the currentcontrol timing causes the air-fuel ratio error estimated value Eaf toconverge to 0.

For example, when NE=NE×3 holds in the current control timing, Wcp₂becomes equal to 1, and the other three link weight functions Wcp_(i)become equal to 0, whereby only the basic local correction valueDlift_bs₂ corresponding to NE=NE×3 is calculated such that it canproperly compensate for a change in the sensitivity of the air-fuelratio error estimated value Eaf. Further, when NE=NE×2, Wcp₁=Wcp₂=0.5,and Wcp₃=Wcp₄=0 hold, whereby the two basic local correction valuesDlift_bs₁ and Dlift_bs₂ are calculated such that the air-fuel ratioerror estimated value Eaf is caused to converge to 0.

The forgetting coefficient λ is used in the algorithm for calculatingthe basic local correction values Dlift_bs_(i) for the following reason:The air-fuel ratio correction coefficient KAF is calculated with thesliding mode control algorithm expressed by the equations (6) to (10),such that the actual air-fuel ratio KACT is caused to converge to thetarget air-fuel ratio KCMD, and the basic local correction valuesDlift_bs_(i) are calculated with the control algorithm to which isapplied the sliding mode control algorithm expressed by the equations(19) to (26), such that the modified errors Weaf_(i) calculated based onthe air-fuel ratio correction coefficient KAF converge to 0. Therefore,unless the forgetting coefficient λ is used, there is a possibility thatthe adaptive law inputs Uadp′ and Uadp_(i) as integral terms in theabove two control algorithms interfere with each other to exhibit anoscillating behavior, or the absolute values of the respective adaptivelaw inputs become very large, causing improper modification of acorrelation model. In these cases, the calculation accuracy of the basiclocal correction value Dlift_bs_(i), i.e. the first estimated intake airamount Gcyl_vt is degraded to degrade controllability in a transientstate.

In contrast, in the aforementioned equation (23), when the absolutevalue of the immediately preceding value Dlift_bs_(i)(k−1) of the basiclocal correction value is large, to avoid an increase in the integralvalue δ_(i) of the switching function of the adaptive law inputUadp_(i), the immediately preceding value δ_(i)(k−1) of the integralvalue of the switching function is multiplied by the forgettingcoefficient λ which is set to a value within a range of 0<λ<1. In thiscase, when the aforementioned equation (23) is expanded by a recurrenceformula thereof, the integral value δ_(i)(k−h) of the switching functioncalculated in control timing h (h is a natural number not smaller than2) times earlier is multiplied by λ^(h) (≈0), so that even when thecalculation process proceeds, it is possible to avoid an increase in theintegral value δ_(i) of the switching function, that is, an increase inthe adaptive law input Uadp_(i). As a result, it is possible to improvethe calculation accuracy of the first estimated intake air amountGcyl_vt, thereby making it possible to improve controllability in atransient state.

Further, if the forgetting coefficient λ is always set to a value withinthe range of 0<λ<1, when the modified error Weaf_(i) takes a value closeto 0, the basic local correction values Dlift_bs_(i) come to converge toa value close to 0 due to a forgetting effect provided by the forgettingcoefficient λ, so that when a control error occurs again in such astate, it takes time to eliminate the control error. Therefore, to avoidthe inconvenience and eliminate the control error quickly, it isnecessary to hold the basic local correction value Dlift_bs_(i) at avalue capable of compensating for the modified error Weaf_(i) even whenthe value of the modified error Weaf_(i) is relatively small. Therefore,in the present embodiment, when the immediately preceding valueDlift_bs_(i)(k−1) of the basic local correction value is within theabove-described range, the forgetting coefficient λ is set to 1 so as tocancel the forgetting effect provided by the forgetting coefficient λ.It should be noted that when the forgetting effect by the forgettingcoefficient λ is always unnecessary, the forgetting coefficient λ may beset to 1 in the equation (23) irrespective of the magnitude of theimmediately preceding value Dlift_bs_(i)(k−1).

Further, the basic local correction value Dlift_bs_(i) is calculated bythe aforementioned equations (19) to (26) such that the modified errorsWeaf_(i) are caused to converge to 0, and hence e.g. when theabove-described basic error weight W_base takes both a positive valueand a negative value, if the basic error weight W_base changes betweenthe positive value and the negative value, the sign of the modifiederror Weaf_(i) is inverted along with the change in the basic errorweight W_base to invert the signs of the respective control inputsUrch_(i), Unl_(i), and Uadp_(i), whereby the basic local correctionvalue Dlift_bs_(i) is calculated as an improper value, which can makethe control unstable. Therefore, to ensure the stability of the control,in the aforementioned FIG. 21, the basic error weight W_base is set to 0under a condition where it takes a negative value.

It should be noted that when the signs of gains of the respectivecontrol inputs Urch_(i), Unl_(i), and Uadp_(i) are controlled to beinverted along with the change in the sign of the basic error weightW_base, even when the basic error weight W_base takes both a positivevalue and a negative value, it is possible to ensure the stability ofcontrol, similarly to the present embodiment. Therefore, in such a case,the values of curves, shown by broken lines in FIG. 21, may be used onwhich the basic error weight W_base takes negative values.

On the other hand, the correction sensitivity-calculating section 126calculates a correction sensitivity Rlift by the following method:First, the correction sensitivity-calculating section 126 calculates asecond corrected valve lift Liftin_mod_p by the aforementioned equation(14).

Then, the correction sensitivity-calculating section 126 calculates abasic sensitivity R_base by searching a map shown in FIG. 23 accordingto the second corrected valve lift Liftin_mod_p and the engine speed NE.Similarly to the above-described basic error weight W_base, the basicsensitivity R_base takes a value obtained by normalizing the ratioΔGcyl/ΔLiftin with reference to the absolute value |ΔGcyl_x/ΔLiftin_x|of the ratio ΔGcyl_x/ΔLiftin_x obtained at a predetermined minute liftand a predetermined low engine speed.

In this map, the basic sensitivity R_base is set to a larger value asthe second corrected valve lift Liftin_mod_p is smaller. The reason forthis is the same as given in the description of the FIG. 21 map.Further, in this map, differently from the basic error weight W_base,the basic sensitivity R_base is configured to assume both a positivevalue and a negative value. This is because as described hereinafter,the lift correction value Dlift is calculated by multiplying the basiclocal correction value Dlift_bs_(i) by the correction sensitivity Rlift,and the corrected valve lift Liftin_mod is calculated by adding the liftcorrection value Dlift to the valve lift Liftin, so that even when thecorrection sensitivity Rlift takes both a positive value and a negativevalue, it is possible to enhance the responsiveness of the air-fuelratio control without spoiling the stability of control.

Further, the correction sensitivity-calculating section 126 calculates asensitivity correction coefficient K_r by searching a map shown in FIG.24 according to the cam phase Cain and the engine speed NE. In FIG. 24,curves indicated by solid lines represent the values of the sensitivitycorrection coefficient K_r, and curves indicated by broken linesrepresent the values of the error weight correction coefficient K_w, forcomparison. As is clear from the comparison between the curves, in thismap, the sensitivity correction coefficient K_r is configured to haveapproximately the same tendency as that of the error weight correctioncoefficient K_w. The reason for this is the same as given in thedescription of the FIG. 22 map. In addition, the value of thesensitivity correction coefficient K_r on an advanced side thereof isset to a value closer to 1 than that of the error weight correctioncoefficient K_w. This is because when the cam phase Cain is controlledto be advanced, the fuel injection amount TOUT is calculated as asmaller value according to a decrease in the intake air amount, so thatwhen the fuel injection amount TOUT is erroneously calculated as a valuesmaller than an appropriate value, the stability of combustion can bedegraded by leaning of the air-fuel mixture. To avoid this problem, themap is configured as described above.

Then, finally, the correction sensitivity Rlift is calculated by thefollowing equation (27).Rlift(k)=R_base(k)·K _(—) r(k)  (27)

As described above, since the correction sensitivity Rlift is calculatedby the same method as employed for the calculation of the error weightW, the correction sensitivity Rlift is calculated not only as a valueindicative of the sensitivity of the air-fuel ratio error estimatedvalue Eaf to the lift error, that is, the degree of influence of thevalve lift Liftin on the air-fuel ratio error estimated value Eaf butalso as a value indicative of the degree of influence of the enginespeed NE and the cam phase Cain on the air-fuel ratio error estimatedvalue Eaf.

It should be noted that as a map for use in calculating the basicsensitivity R_base, the correction sensitivity-calculating section 126may use, in place of the FIG. 23 map, a map in which the basicsensitivity R_base is set according to the valve lift Liftin and theengine speed NE, that is, a map in which the second corrected valve liftLiftin_mod_p represented by the horizontal axis in FIG. 23 is replacedby the valve lift Liftin.

Subsequently, the final value-calculating section 127 calculates a localcorrection value Dlift_lc_(i) by the following equation (28), and thenfinally calculates the lift correction value Dlift by the followingequation (29).

$\begin{matrix}{{{Dlift\_ lc}_{i}(k)} = {{{{Rlift}(k)} \cdot {{Wcp}_{i}(k)} \cdot {Dlift\_ bs}_{i}}(k)}} & (28) \\{{{Dlift}(k)} = {\sum\limits_{i = 1}^{r}{{Dlift\_ lc}_{i}(k)}}} & (29)\end{matrix}$

As described above, the final value-calculating section 127 calculatesfour local correction values Dlift_lc_(i) by multiplying the basic localcorrection values Dlift_bs_(i) by the correction sensitivity Rlift andthe link weight functions Wcp_(i), and calculates the lift correctionvalue Dlift as the total sum of the local correction valuesDlift_lc_(i). As described above, the correction sensitivity Rlift isused as a multiplication value by which the basic local correctionvalues Dlift_bs_(i) are multiplied, whereby the lift correction valueDlift is calculated as a value on which are reflected the degree ofinfluence of the valve lift Liftin, the engine speed NE, and the camphase Cain, on the air-fuel ratio error estimated value Eaf. In thiscase, when the final value-calculating section 127 calculates the localcorrection value Dlift_lc_(i) without using the correction sensitivityRlift under a condition where the sensitivity of the air-fuel ratioerror estimated value Eaf to the lift error is low, there is a fear thata change in the air-fuel ratio error estimated value Eaf isovercompensated for by the local correction value Dlift_lc_(i), but itis possible to avoid the overcompensation by using the correctionsensitivity Rlift.

Further, the lift correction value Dlift is calculated as the total sumof the local correction values Dlift_lc_(i) calculated by using the linkweight functions Wcp_(i) as multiplication values by which the basiclocal correction value Dlift_bs_(i) is multiplied, and therefore thelift correction value Dlift is calculated as a value obtained by asuccessive combination of the four basic local correction valuesDlift_bs_(i). More specifically, the lift correction value Dlift iscalculated such that even when the engine speed NE changes in a state inwhich the four basic local correction values Dlift_bs_(i) are calculatedas values different from each other, the lift correction value Dliftcontinuously changes with the change in the engine speed NE, withoutforming a stepped portion. It should be noted that in the presentembodiment, the local correction values Dlift_lc_(i) correspond to aplurality of second multiplication values, and a plurality ofmultiplication values.

The lift correction value-calculating section 120 calculates the liftcorrection value Dlift by the above-described method. The aforementionedaddition element 114 calculates the corrected valve lift Liftin_mod bythe following equation (30):Liftin_mod(k)=Liftin(k)+Dlift(k)  (30)

As described above, the addition element 114 calculates the correctedvalve lift Liftin_mod by correcting the valve lift Liftin using the liftcorrection value Dlift. In this case, since the basic local correctionvalues Dlift_bs_(i) are values for causing the modified errors Weaf_(i)to converge to 0, correction of the valve lift Liftin using the liftcorrection value Dlift corresponds to correcting or modifying the valvelift Liftin such that the lift error is eliminated. Therefore,calculating the basic estimated intake air amount Gcyl_vt_base bysearching the aforementioned FIG. 11 map according to the correctedvalve lift Liftin_mod thus calculated corresponds to calculating thefirst estimated intake air amount Gcyl_vt as the first input value byusing a map modified such that the lift error is eliminated, that is, acorrelation model.

Next, a control process carried out by the ECU 2 at the above-describedcontrol period ΔTn will be described with reference to FIG. 25. Itshould be noted that various calculated values referred to in thefollowing description are assumed to be stored in the RAM of the ECU 2.

In this process, first, in a step 1 (shown as S1 in abbreviated form inFIG. 25; the following steps are also shown in abbreviated form), thecounter value C_TDC of a TDC counter is set to the sum (C_TDCZ+1) of theimmediately preceding value C_TDCZ of the counter value C_TDC and 1.This means that the counter value C_TDC of the TDC counter isincremented by 1.

Then, the process proceeds to a step 2, wherein it is determined whetheror not C_TDC=4 holds. If the answer to this question is negative (NO),i.e. if C_TDC≠4 holds, the process proceeds to a step 6, describedhereinafter. On the other hand, if the answer to this question isaffirmative (YES), the process proceeds to a step 3, wherein the countervalue C_TDC of the TDC counter is reset to 0.

In a step 4 following the step 3, the target air-fuel ratio KCMD iscalculated. More specifically, as described above, the target air-fuelratio KCMD is calculated by searching the map shown in FIG. 14 accordingto the calculated intake air amount Gcyl and the accelerator pedalopening AP.

Then, in a step 5, the air-fuel ratio correction coefficient KAF iscalculated. More specifically, the air-fuel ratio correction coefficientKAF is calculated with the control algorithm expressed by theaforementioned equations (6) to (10) if conditions for executingair-fuel ratio feedback control are satisfied. On the other hand, if theconditions for executing air-fuel ratio feedback control are notsatisfied, the air-fuel ratio correction coefficient KAF is set to 1.

In the step 6 following the step 2 or 5, an air-fuel ratio controlprocess is executed. The air-fuel ratio control process is provided forcalculating the fuel injection amount TOUT for each fuel injection valve10, and detailed description thereof will be given hereinafter.

Subsequently, in a step 7, an ignition timing control process isperformed. In this process, the ignition timing Iglog is calculated bythe same method as employed in the ignition timing control processdisclosed in Japanese Laid-Open Patent Publication (Kokai) No.2005-315161 referred to hereinabove, though detailed description thereofis omitted here. After that, the present process is terminated.

As described above, in the FIG. 25 control process, the steps 3 to 5 arecarried out whenever C_TDC=4 holds, and hence they are carried outwhenever the total of four successive pulses of the TDC signal aregenerated, i.e. every combustion cycle.

Next, the aforementioned air-fuel ratio control process will bedescribed with reference to FIG. 26. As will be described hereinafter,the present process is for calculating the fuel injection amount TOUTfor each fuel injection valve 10. More specifically, the present processis for calculating the fuel injection amounts TOUT for the fuelinjection valves 10 for the respective cylinders in the order of a firstcylinder→a third cylinder→a fourth cylinder→a second cylinder, as thecounter value C_TDC of the TDC counter is incremented from 1 to 4.

First, in a step 20, the aforementioned corrected valve lift Liftin_mod,air-fuel ratio correction coefficient KAF, and various parameters areread in. In this case, the corrected valve lift Liftin_mod is calculatedat the control period ΔTn, as described above, and hence the reading ofthe corrected valve lift Liftin_mod corresponds to the downsampling ofthe same. Further, since the air-fuel ratio correction coefficient KAFis calculated every combustion cycle, the reading of the air-fuel ratiocorrection coefficient KAF corresponds to the oversampling of the same.

Then, in a step 21, the basic fuel injection amount Tcyl_bs iscalculated. The process for calculating the basic fuel injection amountTcyl_bs is performed as shown in FIG. 27. More specifically, first, in astep 30, the second estimated intake air amount Gcyl_afm is calculatedby the aforementioned equation (3).

Then, in a step 31, as described heretofore, the basic estimated intakeair amount Gcyl_vt_base is calculated by searching the FIG. 11 mapaccording to the engine speed NE and the corrected valve liftLiftin_mod.

In a step 32 following the step 31, as described heretofore, thecorrection coefficient K_gcyl_vt is calculated by searching the FIG. 12map according to the engine speed NE and the cam phase Cain.

After that, the process proceeds to a step 33, wherein the firstestimated intake air amount Gcyl_vt is calculated by the aforementionedequation (1) based on the two values Gcyl_vt_base and K_gcyl_vtcalculated in the steps 31 and 32.

Next, in a step 34, the estimated flow rate Gin_vt is calculated by theaforementioned equation (2), and thereafter the process proceeds to astep 35, wherein it is determined whether or not a variable mechanismfailure flag F_VDNG is equal to 1.

The variable mechanism failure flag F_VDNG is set to 1 when it isdetermined in a failure determination process, not shown, that at leastone of the variable valve lift mechanism 50 and the variable cam phasemechanism 70 is faulty, and to 0 when it is determined that themechanisms 50 and 70 are both normal. It should be noted that in thefollowing description, the variable valve lift mechanism 50 and thevariable cam phase mechanism 70 are collectively referred to as “the twovariable mechanisms”.

If the answer to the question of the step 35 is negative (NO), i.e. ifboth of the two variable mechanisms are normal, the process proceeds toa step 36, wherein it is determined whether or not an air flow sensorfailure flag F_AFMNG is equal to 1. The air flow sensor failure flagF_AFMNG is set to 1 when it is determined in a failure determinationprocess, not shown, that the air flow sensor 22 is faulty, and to 0 whenit is determined that the air flow sensor 22 is normal.

If the answer to the question of the step 36 is negative (NO), i.e. ifthe air flow sensor 22 is normal, the process proceeds to a step 37,wherein as described above, the transition coefficient Kg is calculatedby searching the FIG. 13 map according to the estimated flow rateGin_vt.

On the other hand, if the answer to the question of the step 36 isaffirmative (YES), i.e. if the air flow sensor 22 is faulty, the processproceeds to a step 38, wherein the transition coefficient Kg is set to0.

In a step 39 following the step 37 or 38, the calculated intake airamount Gcyl is calculated by the aforementioned equation (4). Then, in astep 40, the basic fuel injection amount Tcyl_bs is set to the productKgt·Gcyl of the conversion coefficient and the calculated intake airamount Gcyl, followed by terminating the present process.

On the other hand, if the answer to the question of the step 35 isaffirmative (YES), i.e. if it is determined that at least one of the twovariable mechanisms is faulty, the process proceeds to a step 41,wherein the calculated intake air amount Gcyl is set to theaforementioned predetermined failure-time value Gcyl_fs. Then, theaforementioned step 40 is executed, followed by terminating the presentprocess.

Referring again to FIG. 26, in the step 21, the basic fuel injectionamount Tcyl_bs is calculated, as described above, and then the processproceeds to a step 22, wherein the total correction coefficient KTOTALis calculated. More specifically, as described above, the totalcorrection coefficient KTOTAL is calculated by calculating variouscorrection coefficients by searching respective associated mapsaccording to operating parameters (e.g. the intake air temperature TA,the atmospheric pressure PA, the engine coolant temperature TW, theaccelerator pedal opening AP, etc.), and then multiplying the thuscalculated correction coefficients by each other.

Next, the process proceeds to a step 23, wherein the demanded fuelinjection amount Tcyl is calculated by the aforementioned equation (11).Then, in a step 24, the fuel injection amount TOUT is calculated bycarrying out a predetermined fuel attachment-dependent correctionprocess on the demanded fuel injection amount Tcyl, as described above,followed by terminating the present process. Thus, each fuel injectionvalve 10 is controlled such that the fuel injection timing and thevalve-opening time period thereof assume values determined based on thefuel injection amount TOUT. As a result, if the conditions for executingthe air-fuel ratio feedback control are satisfied, the actual air-fuelratio KACT is controlled such that it converges to the target air-fuelratio KCMD.

Next, a control process executed by the ECU 2 at the control period ΔTkset by a timer will be described with reference to FIG. 28. In thisprocess, first, in a step 50, data stored in the RAM, such as the firstestimated intake air amount Gcyl_vt, the second estimated intake airamount Gcyl_afm, the actual air-fuel ratio KACT, and the air-fuel ratiocorrection coefficient KAF, are read in.

Then, the process proceeds to a step 51, wherein it is determinedwhether or not a feedback control execution flag F_AFFB is equal to 1.The feedback control execution flag F_AFFB is set to 1 during executionof the air-fuel ratio feedback control, and otherwise to 0.

If the answer to the question of the step 51 is affirmative (YES), i.e.if the air-fuel ratio feedback control is being executed, the processproceeds to a step 52, wherein it is determined whether or not theengine coolant temperature TW is higher than a predetermined referencevalue TWREF. The predetermined reference value TWREF is a value fordetermining whether or not the warmup operation of the engine 3 has beenterminated.

If the answer to the question of the step 52 is affirmative (YES), i.e.if the warmup operation of the engine 3 has been terminated, the processproceeds to a step 53, wherein it is determined whether or not a purgecompletion flag F_CANI is equal to 1. The purge completion flag F_CANIis set to 1 when a purge operation for returning evaporated fueladsorbed by a canister into a intake passage has been completed, andotherwise to 0.

If the answer to the question of the step 53 is affirmative (YES), i.e.if the purge operation has been completed, the process proceeds to astep 54, wherein a process for calculating the corrected valve liftLiftin_mod is carried out. The process for calculating the correctedvalve lift Liftin_mod will be described in detail hereinafter.

On the other hand, if any of the answers to the questions of the steps51 to 53 is negative (NO), it is judged that conditions for calculatingthe corrected valve lift Liftin_mod are not satisfied, and the processproceeds to a step 56, wherein the corrected valve lift Liftin_mod isset to the immediately preceding value Liftin_modz thereof. As describedabove, if the air-fuel ratio feedback control is not being executed, ifthe warmup operation of the engine 3 has not been terminated, or if thepurge operation has not been completed, the air-fuel ratio controlbecomes unstable, and the calculation accuracy of the lift correctionvalue Dlift is lowered, which can lower the calculation accuracy of thecorrected valve lift Liftin_mod. To avoid this problem, the immediatelypreceding value of the corrected valve lift Liftin_mod is used withoutupdating the corrected valve lift Liftin_mod.

In a step 55 following the step 54 or 56, a variable mechanism controlprocess is performed, as described hereinafter, followed by terminatingthe present process.

Next, the above-described process for calculating the corrected valvelift Liftin_mod will be described with reference to FIG. 29. First, in astep 60, the air-fuel ratio error estimated value Eaf is calculated bythe aforementioned equations (12) and (13).

Then, the process proceeds to a step 61, wherein the values of the linkweight functions Wcp_(i) are calculated by searching the aforementionedFIG. 20 map according to the engine speed NE. After that, the processproceeds to a step 62, wherein the second corrected valve liftLiftin_mod_p is calculated by the aforementioned equation (14).

In a step 63 following the step 62, the basic error weight W_base iscalculated by searching the aforementioned FIG. 21 map according to thesecond corrected valve lift Liftin_mod_p and the engine speed NE. Then,in a step 64, the error weight correction coefficient K_w is calculatedby searching the aforementioned FIG. 22 map according to the cam phaseCain and the engine speed NE.

Next, in a step 65, the error weight W is calculated by theaforementioned equation (15), whereafter the process proceeds to a step66, wherein the modified error Weaf_(i) is calculated by theaforementioned equations (16) to (18).

In a step 67 following the step 66, the basic local correction valueDlift_bs_(i) is calculated by the aforementioned equations (19) to (26),and then the process proceeds to a step 68, wherein the basicsensitivity R_base is calculated by searching the aforementioned FIG. 23map according to the second corrected valve lift Liftin_mod_p and theengine speed NE.

Then, the process proceeds to a step 69, wherein the sensitivitycorrection coefficient K_r is calculated by searching the aforementionedFIG. 24 map according to the cam phase Cain and the engine speed NE.After that, in a step 70, the correction sensitivity Rlift is calculatedby the aforementioned equation (27).

In a step 71 following the step 70, the lift correction value Dlift iscalculated by the aforementioned equations (28) and (29). Next, theprocess proceeds to a step 72, wherein the corrected valve liftLiftin_mod is calculated by the aforementioned equation (30), followedby terminating the present process.

Next, the aforementioned variable mechanism control process will bedescribed with reference to FIG. 30. The present process is forcalculating the two control inputs U_Liftin and U_Cain for controllingthe two variable mechanisms, respectively.

In this process, first, it is determined in a step 80 whether or not theaforementioned variable mechanism failure flag F_VDNG is equal to 1. Ifthe answer to this question is negative (NO), i.e. if the two variablemechanisms are both normal, the process proceeds to a step 81, whereinit is determined whether or not the engine start flag F_ENGSTART isequal to 1.

The above engine start flag F_ENGSTART is set by determining in adetermination process, not shown, whether or not engine start control isbeing executed, i.e. the engine 3 is being cranked, based on the enginespeed NE and the ON/OFF signal output from an IG·SW 29. Morespecifically, when the engine start control is being executed, theengine start flag F_ENGSTART is set to 1, and otherwise set to 0.

If the answer to the question of the step 81 is affirmative (YES), i.e.if the engine start control is being executed, the process proceeds to astep 82, wherein the target valve lift Liftin_cmd is calculated bysearching a map shown in FIG. 31 according to the engine coolanttemperature TW.

In this map, in the range where the engine coolant temperature TW ishigher than a predetermined value TWREF1, the target valve liftLiftin_cmd is set to a larger value as the engine coolant temperature TWis lower, and in the range where TW≦TWREF1 holds, the target valve liftLiftin_cmd is set to a predetermined value Liftinref. This is tocompensate for an increase in friction of the variable valve liftmechanism 50, which is caused when the engine coolant temperature TW islow.

Then, in a step 83, the target cam phase Cain_cmd is calculated bysearching a map shown in FIG. 32 according to the engine coolanttemperature TW.

In this map, in the range where the engine coolant temperature TW ishigher than a predetermined value TWREF2, the target cam phase Cain_cmdis set to a more retarded value as the engine coolant temperature TW islower, and in the range where TW≦TWREF2 holds, the target cam phaseCain_cmd is set to a predetermined value Cainref. This is to ensure thecombustion stability of the engine 3 by controlling the cam phase Cainto a more retarded value when the engine coolant temperature TW is lowthan when the engine coolant temperature TW is high, to thereby reducethe valve overlap, to increase the flow velocity of intake air.

Next, the process proceeds to a step 84, wherein the lift control inputU_Liftin is calculated with a target value filter-typetwo-degree-of-freedom response-specifying control algorithm expressed bythe following equations (31) to (34).

$\begin{matrix}{{{U\_ Liftin}(k)} = {{{{- {Krch\_ lf}} \cdot {\sigma\_ lf}}(k)} - {{Kadp\_ lf} \cdot {\sum\limits_{i = 0}^{k}{{\sigma\_ lf}(i)}}}}} & (31) \\{{{\sigma\_ lf}(k)} = {{{E\_ lf}(k)} + {{{pole\_ lf} \cdot {E\_ lf}}\left( {k - 1} \right)}}} & (32) \\{{{E\_ lf}(k)} = {{{Liftin\_ mod}(k)} - {{Liftin\_ cmd}{\_ f}(k)}}} & (33) \\{{{Liftin\_ cmd}{\_ f}(k)} = {{{- {pole\_ f}}{{\_ lf} \cdot {Liftin\_ cmd}}{\_ f}\left( {k - 1} \right)} + {{\left( {1 + {{pole\_ f}{\_ lf}}} \right) \cdot {Liftin\_ cmd}}(k)}}} & (34)\end{matrix}$

In the equation (31), Krch_lf and Kadp_lf represent a predeterminedreaching law gain and a predetermined adaptive law gain, respectively.Furthermore, σ_lf represents a switching function defined by theequation (32). In the equation (32), pole_lf represents a switchingfunction-setting parameter set to a value which satisfies therelationship of −1<pole_lf<0, and E_lf represents a follow-up errorcalculated by the equation (33). In the equation (33), Liftin_cmd_frepresents a filtered value of the target valve lift, and is calculatedwith a first-order lag filter algorithm expressed by the equation (34).In the equation (34), pole_f_lf represents a target value filter-settingparameter set to a value which satisfies the relationship of−1<pole_f_lf<0.

Next, the process proceeds to a step 85, wherein the phase control inputU_Cain is calculated with a target value filter-typetwo-degree-of-freedom response-specifying control algorithm expressed bythe following equations (35) to (38).

$\begin{matrix}{{{U\_ Cain}(k)} = {{{{- {Krch\_ ca}} \cdot {\sigma\_ ca}}(k)} - {{Kadp\_ ca} \cdot {\sum\limits_{i = 0}^{k}{{\sigma\_ ca}(i)}}}}} & (35) \\{{{\sigma\_ ca}(k)} = {{{E\_ ca}(k)} + {{{pole\_ ca} \cdot {E\_ ca}}\left( {k - 1} \right)}}} & (36) \\{{{E\_ ca}(k)} = {{\text{Cain}(k)} - {{Cain\_ cmd}{\_ f}(k)}}} & (37) \\{{{Cain\_ cmd}{\_ f}(k)} = {{{- {pole\_ f}}{{\_ ca} \cdot {Cain\_ cmd}}{\_ f}\left( {k - 1} \right)} + {{\left( {1 + {{pole\_ f}{\_ ca}}} \right) \cdot {Cain\_ cmd}}(k)}}} & (38)\end{matrix}$

In the equation (35), Krch_ca and Kadp_ca represent a predeterminedreaching law gain and a predetermined adaptive law gain, respectively.Furthermore, σ_ca represents a switching function defined by theequation (36). In the equation (36), pole_ca represents a switchingfunction-setting parameter set to a value which satisfies therelationship of −1<pole_ca<0, and E_ca represents a follow-up errorcalculated by the equation (37). In the equation (37), Cain_cmd_frepresents a filtered value of the target cam phase, and is calculatedwith a first-order lag filter algorithm expressed by the equation (38).In the equation (38), pole_f_ca represents a target value filter-settingparameter set to a value which satisfies the relationship of−1<pole_f_ca<0.

In the step 85, the phase control input U_Cain is calculated as above,followed by terminating the present process.

On the other hand, if the answer to the question of the step 81 isnegative (NO), i.e. if the engine start control is not being executed,the process proceeds to a step 86, wherein it is determined whether ornot the accelerator pedal opening AP is smaller than a predeterminedvalue APREF. If the answer to this question is affirmative (YES), i.e.if the accelerator pedal is not stepped on, the process proceeds to astep 87, wherein it is determined whether or not the count Tast of anafter-start timer is smaller than a predetermined value Tastlmt.

If the answer to this question is affirmative (YES), i.e. ifTast<Tastlmt holds, it is judged that the catalyst warmup control shouldbe executed, and the process proceeds to a step 88, wherein the targetvalve lift Liftin_cmd is calculated by searching a map shown in FIG. 33according to the count Tast of the after-start timer and the enginecoolant temperature TW. In FIG. 33, TW1 to TW3 represent predeterminedvalues of the engine coolant temperature TW, which satisfy therelationship of TW1<TW2<TW3. This also applies to the followingdescription.

In this map, the target valve lift Liftin_cmd is set to a larger valueas the engine coolant temperature TW is lower. This is because as theengine coolant temperature TW is lower, it takes a longer time period toactivate the catalyst, and hence the volume of exhaust gasses isincreased to shorten the time period required for activating thecatalyst. Furthermore, in the above map, the target valve liftLiftin_cmd is set to a larger value as the count Tast of the after-starttimer becomes larger in the range where the count Tast is small, whereasin a region where the count Tast is large to a certain or more extent,the target valve lift Liftin_cmd is set to a smaller value as the countTast becomes larger. This is because the warming up of the engine 3proceeds along with the lapse of the execution time period of thecatalyst warmup control, so that after friction lowers, unless theintake air amount is reduced, the ignition timing is excessivelyretarded so as to hold the engine speed NE at the target value, whichmakes unstable the combustion state of the engine. To avoid thecombustion state from being unstable, the map is configured as describedabove.

Then, in a step 89, the target cam phase Cain_cmd is calculated bysearching a map shown in FIG. 34 according to the count Tast of theafter-start timer and the engine coolant temperature TW.

In this map, the target cam phase Cain_cmd is set to a more advancedvalue as the engine coolant temperature TW is lower. This is because asthe engine coolant temperature TW is lower, it takes a longer timeperiod to activate the catalyst, as described above, and hence thepumping loss is reduced to increase the intake air amount to therebyshorten the time period required for activating the catalyst.Furthermore, in the above map, the target cam phase Cain_cmd is set to amore retarded value as the count Tast of the after-start timer becomeslarger in the range where the count Tast of the after-start timer issmall, whereas in a region where the count Tast is large to a certain ormore extent, the target cam phase Cain_cmd is set to a more advancedvalue as the count Tast of the after-start timer is larger. The reasonfor this is the same as given in the description of the FIG. 33 map.

Then, the steps 84 and 85 are carried out, as described hereinabove,followed by terminating the present process.

On the other hand, if the answer to the question of the step 86 or 87 isnegative (NO), i.e. if the accelerator pedal is stepped on, or ifTast≧Tastlmt holds, the process proceeds to a step 90, wherein thetarget valve lift Liftin_cmd is calculated by searching a map shown inFIG. 35 according to the engine speed NE and the accelerator pedalopening AP. In FIG. 35, AP1 to AP3 indicate predetermined values of theaccelerator pedal opening AP which satisfy the relationship ofAP1<AP2<AP3. This also applies to the following description.

In this map, the target valve lift Liftin_cmd is set to a larger valueas the engine speed NE is higher, or as the accelerator pedal opening APis larger. This is because as the engine speed NE is higher, or as theaccelerator pedal opening AP is larger, an output required of the engine3 is larger, and hence a larger intake air amount is required.

Then, in a step 91, the target cam phase Cain_cmd is calculated bysearching a map shown in FIG. 36 according to the engine speed NE andthe accelerator pedal opening AP. In this map, when the acceleratorpedal opening AP is small and the engine speed NE is in the medium speedregion, the target cam phase Cain_cmd is set to a more advanced valuethan otherwise. This is because under the above operating conditions ofthe engine 3, it is necessary to reduce the pumping loss.

Following the step 91, the steps 84 and 85 are carried out, as describedhereinabove, followed by terminating the present process.

On the other hand, if the answer to the question of the step 80 isaffirmative (YES), i.e. if at least one of the two variable mechanismsis faulty, the process proceeds to a step 92, wherein the lift controlinput U_Liftin is set to the predetermined failure time valueU_Liftin_fs, and the phase control input U_Cain to the predeterminedfailure time value U_Cain_fs, followed by terminating the presentprocess. As a result, as described above, the valve lift Liftin is heldat the predetermined locked value, and the cam phase Cain at thepredetermined locked value, whereby it is possible to suitably carry outidling or starting of the engine 3 during stoppage of the vehicle, andat the same time hold the vehicle in the state of low-speed travelingwhen the vehicle is traveling.

In the present process, the lift control input U_liftin and the phasecontrol input U_Cain are calculated as described above. Then, byinputting these control inputs U_Liftin and U_Cain to the variable valvelift mechanism 50 and the variable cam phase mechanism 70, respectively,the intake air amount is controlled.

Next, a description will be given of the results of control by thecontrol apparatus 1 according to the first embodiment configured asdescribed above. FIG. 37 shows an example of the results of the air-fuelratio control carried out by the control apparatus 1 according to thepresent embodiment. For comparison, FIG. 38 shows an example(hereinafter referred to as “the comparative example”) of controlresults obtained when the lift correction value Dlift is held at 0, i.e.when Liftin_mod is set to be equal to Liftin. It should be noted thatthe above control results are obtained by setting the target air-fuelratio KCMD to 1 for ease of understanding.

Referring to FIGS. 37 and 38, it is understood that in the FIG. 38comparative example, there often occurs a state in which the air-fuelratio correction coefficient KAF largely deviates from the targetair-fuel ratio KCMD toward the richer side, and is held on the richerside. In contrast, it is understood that in the FIG. 37 example of thecontrol results by the control apparatus 1 according to the presentembodiment, the air-fuel ratio correction coefficient KAF is held in thevicinity of the target air-fuel ratio KCMD and that high-level controlaccuracy can be ensured.

Further, when the differences between the target air-fuel ratios KCMDand the actual air-fuel ratios KACT, that is, errors of the air-fuelratios of the example and the comparative example are compared with eachother by referring to FIGS. 37 and 38, it is understood that relativelylarge air-fuel ratio errors occur frequently in the comparative example.In contrast, it is understood that in the example of the control resultsaccording to the present embodiment, air-fuel ratio errors arecontrolled to smaller values than the values of the air-fuel ratioerrors in the comparative example, whereby high-level control accuracycan be secured. As described above, it is understood that by using thelift correction value Dlift according to the present embodiment, it ispossible to accurately compensate for the lift error, thereby making itpossible to ensure high control accuracy in the air-fuel ratio control.

As described hereinabove, according to the control apparatus 1 of thefirst embodiment, the air-fuel ratio error estimated value Eafindicative of the control error is calculated based on the actualair-fuel ratio KACT and the target air-fuel ratio KCMD; the link weightfunctions Wcp_(i) are calculated by searching the FIG. 20 map accordingto the engine speed NE; and the modified errors Weaf_(i) are calculatedby multiplying the air-fuel ratio error estimated value Eaf by the linkweight functions Wcp_(i), the error weight W, and the transitioncoefficient weight Wkg. Further, the basic local correction valuesDlift_bs_(i) are calculated such that the modified errors Weaf_(i) thusobtained are caused to converge to 0 (i.e. such that the air-fuel ratioerror estimated value Eaf is caused to converge to 0 as thepredetermined target value); the local correction values Dlift_lc_(i)are calculated by multiplying the basic local correction valuesDlift_bs_(i) by the correction sensitivity Rlift and the link weightfunctions Wcp_(i); the lift correction value Dlift is calculated as thetotal sum of the local correction values Dlift_lc_(i); and the firstestimated intake air amount Gcyl_vt is calculated using the correctedvalve lift Liftin_mod obtained by correcting the valve lift Liftin bythe above lift correction value Dlift, and the map in FIG. 11.

More specifically, since the first estimated intake air amount Gcyl_vtis calculated using the correlation model which is modified such thatthe air-fuel ratio error estimated value Eaf is caused to converge to 0,it is possible to properly compensate for the lift error, i.e. thecontrol error by the thus calculated first estimated intake air amountGcyl_vt, not only when the control error is temporarily increased by adisturbance but also under a condition where the lift error istemporarily increased e.g. by the degradation of reliability of thedetection results of the valve lift Liftin and/or the engine speed NE, achange in the dynamic characteristics of the variable valve liftmechanism 50. In addition, since the map search method generallyemployed in the feedforward control method is employed for thecorrelation model, the control error can be compensated for more quicklythan when the control error is compensated for by the air-fuel ratiofeedback control using the air-fuel ratio correction coefficient KAF.

Further, the modified errors Weaf_(i) are calculated by multiplying theair-fuel ratio error estimated value Eaf by the link weight functionsWcp_(i), the error weight W, and the transition coefficient weight Wkg.Further, as described above, the four link weight functions Wcp_(i) arecalculated such that they are associated with the four regions formed bydividing the region where the engine speed NE is variable. Further, thefour link weight functions Wcp_(i) are set to positive values not largerthan 1 in the associated regions, and set to 0 in regions other than theassociated regions, while the sum of the values of the link weightfunctions Wcp_(i) associated with the regions overlapping each other isset to be equal to the maximum value 1 of each link weight functionWcp_(i). This makes it possible to distribute the air-fuel ratio errorestimated value Eaf to the four basic local correction valuesDlift_bs_(i) via the four link weight functions Wcp_(i), thereby makingit possible to properly reduce the degree of deviation of thecorrelation model in each of the four regions. Particularly even whendeviation of the correlation model from the actual correlation of theengine speed NE and the valve lift Liftin with the basic estimatedintake air amount Gcyl_vt_base is different between the four regions ofthe engine speed NE in respect of the direction of change in thedeviation, it is possible to properly modify the correlation model on anregion-by-region basis while coping with the deviation.

Further, the local correction values Dlift_lc_(i) are calculated bymultiplying the basic local correction values Dlift_bs_(i) by thecorrection sensitivity Rlift and the link weight functions Wcp_(i), andthe lift correction value Dlift is calculated as the total sum of theabove local correction values Dlift_lc_(i). Therefore, the liftcorrection value Dlift can be calculated as a value obtained by asuccessive combination of the four basic local correction valuesDlift_bs_(i). Thus, even when the engine speed NE suddenly changes in astate in which the four basic local correction values Dlift_bs_(i) aredifferent from each other, the lift correction value Dlift can becalculated such that it can change continuously with the sudden changein the engine speed NE. Therefore, by using the corrected valve liftLiftin_mod obtained by correcting the valve lift Liftin by the thuscalculated lift correction value Dlift (i.e. by modifying thecorrelation model), the first estimated intake air amount Gcyl_vt can becalculated such that it changes in a smooth and stepless manner evenwhen the engine speed NE suddenly changes. As a result, even under acondition where the air-fuel ratio error estimated value Eaf, i.e. thecontrol error is temporarily increased by a sudden change in the enginespeed NE, it is possible to avoid a sudden improper change or a suddenstepped change in the first estimated intake air amount Gcyl_vt, therebymaking it possible to enhance the accuracy and stability of control.

Further, the error weight W is calculated such that it reflects thedegree of influence of the cam phase Cain and the engine speed NE on theair-fuel ratio error estimated value Eaf, and hence if the thuscalculated error weight W is used, the first estimated intake air amountGcyl_vt can be calculated as a value reflecting the degree of influenceof the cam phase Cain and the engine speed NE on the air-fuel ratioerror estimated value Eaf. In addition, the correction sensitivity Rliftis calculated as a value indicative of the sensitivity of the air-fuelratio error estimated value Eaf to the lift error, and therefore, byusing the thus calculated correction sensitivity Rlift, it is possiblenot only to calculate the first estimated intake air amount Gcyl_vt as avalue reflecting the sensitivity of the air-fuel ratio error estimatedvalue Eaf to the lift error, but also to prevent the lift correctionvalue Dlift from overcompensating for the air-fuel ratio error estimatedvalue Ea under the condition where the sensitivity of the air-fuel ratioerror estimated value Eaf to the lift error is low. From the above, itis possible to enhance the compensation accuracy of the first estimatedintake air amount Gcyl_vt for compensating for the air-fuel ratio errorestimated value Eaf, that is, the air-fuel ratio error, thereby makingit possible to further enhance the control accuracy.

It should be noted that although in the first embodiment, the controlalgorithm expressed by the aforementioned equations (19) to (26) is usedfor the algorithm for calculating the basic local correction valueDlift_bs_(i), by way of example, this is not limitative, but the basiclocal correction value Dlift_bs_(i) may be calculated with a controlalgorithm expressed by the following equations (39) to (47), to whichare applied a combination of an adaptive disturbance observer and asliding mode control algorithm.

$\begin{matrix}{{\sigma_{i}(k)} = {{{Weaf}_{i}(k)} + {S \cdot {{Weaf}_{i}\left( {k - 1} \right)}}}} & (39) \\{{{Urch}_{i}(k)} = {{- {Krch}} \cdot {\sigma_{i}(k)}}} & (40) \\{{{Unl}_{i}(k)} = {{- {Knl}} \cdot {{sgn}\left( {\sigma_{i}(k)} \right)}}} & (41) \\{{\sigma_{i}{\_ hat}(k)} = {{{Urch}_{i}\left( {k - 1} \right)} + {{Unl}_{i}\left( {k - 1} \right)} + {{Uls}_{i}\left( {k - 1} \right)}}} & (42) \\\begin{matrix}{{{E\_ sig}_{i}(k)} = {{\sigma_{i}(k)} - {\sigma_{i}{\_ hat}(k)}}} \\{= {{\sigma_{i}(k)} - {{Urch}_{i}\left( {k - 1} \right)} - {{Unl}_{i}\left( {k - 1} \right)} - {{Uls}_{i}\left( {k - 1} \right)}}}\end{matrix} & (43) \\{{{Uls}_{i}(k)} = {{\lambda \cdot {{Uls}_{i}\left( {k - 1} \right)}} + {\frac{P}{1 + P}{E\_ sig}_{i}(k)}}} & (44) \\{{{*{When}\mspace{14mu}{Dlift\_ bs}{\_ L}} < {{Dlift\_ bs}_{i}\left( {k - 1} \right)} < {{Dlift\_ bs}{\_ H}}}{\lambda = 1}} & (45) \\{{{*{When}\mspace{14mu}{Dlift\_ bs}_{i}\left( {k - 1} \right)} \leqq {{Dlift\_ bs}{\_ L}\mspace{14mu}{or}\mspace{14mu}{Dlift\_ bs}{\_ H}} \leqq {{Dlift\_ bs}_{i}\left( {k - 1} \right)}}{\lambda = {\lambda\;{lmt}}}} & (46) \\{{{Dlift\_ bs}_{i}(k)} = {{{Urch}_{i}(k)} + {{Unl}_{i}(k)} + {{Uls}_{i}(k)}}} & (47)\end{matrix}$

In the above equation (42), σ_(i) _(—) hat represents an estimated valueof a switching function, and Uls_(i) a disturbance estimated value. Thedisturbance estimated value Uls_(i) is calculated with a fixed gainidentification algorithm expressed by the equations (43) and (44). Inthe equation (43), E_sig_(i) represents an estimation error. In theequation (44), P represents a fixed identification gain. It should benoted that the above equations (42) to (46) express an algorithm forcalculating the disturbance estimated value Uls_(i) of the adaptivedisturbance observer.

In the above algorithm expressed by the equations (39) to (47) forcalculation of the basic local correction value Dlift_bs_(i), thedisturbance estimated value Uls_(i) corresponds to an integral term. Inthe equation (44), the immediately preceding value Uls_(i)(k−1) of thedisturbance estimated value is multiplied by the forgetting coefficientλ, and if the absolute value of the basic local correction valueDlift_bs_(i) is large, the forgetting coefficient λ is set to a valuewithin the range of 0<λ<1. Thus, the aforementioned forgetting effectprovided by the forgetting coefficient λ makes it possible to preventthe integral terms Uadp′ and Uadp_(i) in the control algorithms forcalculating the air-fuel ratio correction coefficient KAF and the basiclocal correction values Dlift_bs_(i) from interfering with each other tothereby prevent the integral terms from exhibiting oscillatingbehaviors, and the absolute values of the respective integral terms frombecoming very large. This makes it possible to avoid impropermodification of the correlation model. As a result, the calculationaccuracy of the first estimated intake air amount Gcyl_vt can beenhanced, thereby making it possible to improve controllability in atransient state. Further, if the absolute value of the immediatelypreceding value Dlift_bs_(i)(k−1) of the basic local correction value issmall, the forgetting coefficient λ is set to 1, and hence even when themodified errors Weaf_(i) become close to 0, the basic local correctionvalues Dlift_bs_(i) can be held at proper values. This makes it possibleto enhance the responsiveness of the air-fuel ratio control when themodified errors Weaf_(i) start to increase, thereby making it possibleto enhance the control accuracy.

In addition, since the disturbance estimated value Uls_(i) is calculatedwith the fixed gain identification algorithm of the adaptive disturbanceobserver, compared with the control algorithm according to the firstembodiment using the adaptive law input Uadp_(i), it is possible tofurther enhance the capability of suppressing the integral fluctuationbehavior and the overshooting behavior of the basic local correctionvalues Dlift_bs_(i).

Further, although in the first embodiment, the basic local correctionvalue Dlift_bs_(i) is calculated using the control algorithm to which isapplied the sliding mode control algorithm expressed by the equations(19) to (26) as the response-specifying control algorithm, by way ofexample, a control algorithm to which is applied a back-stepping controlalgorithm may be used as the response-specifying control algorithm. Whenthe control algorithm to which is applied the back-stepping controlalgorithm is used for the algorithm for calculating the basic localcorrection value Dlift_bs_(i) as well, as described above, it ispossible to obtain the same advantageous effects as provided by thecontrol algorithm expressed by the equations (19) to (26) in the firstembodiment.

Further, although in the first embodiment, the control algorithmexpressed by the aforementioned equations (19) to (26) is used for thealgorithm for calculating the basic local correction value Dlift_bs_(i),by way of example, the algorithm for calculating the basic localcorrection value Dlift_bs_(i) is not limited to this, but any suitablealgorithm may be used insofar as it is capable of calculating the basiclocal correction value Dlift_bs_(i) such that the modified errorWeaf_(i) is caused to converge to 0. For example, a PID controlalgorithm, an optimum control algorithm, an H^(∞) control algorithm, orthe like may be used for the algorithm for calculating the basic localcorrection value Dlift_bs_(i). When the basic local correction valueDlift_bs_(i) is thus calculated with the PID control algorithm, theoptimum control algorithm, the H^(∞) control algorithm, or the like,compared with the control algorithm expressed by the equations (19) to(26), there is a fear that the effect of preventing the modified errorWeaf_(i) from overshooting 0, or the robustness of the control apparatusis degraded, and hence in this respect, the control algorithm accordingto the first embodiment is superior to the PID control algorithm, theoptimum control algorithm, the H^(∞) control algorithm, and so forth.

Further, although in the first embodiment, the control algorithmexpressed by the aforementioned equations (6) to (10) is used for apredetermined feedback control algorithm for calculating the air-fuelratio correction coefficient KAF as the second input value, by way ofexample, the predetermined feedback control algorithm for calculatingthe second input value in the present invention is not limited to this,but any suitable feedback control algorithm may be used insofar as it iscapable of calculating the second input value such that the second inputvalue is caused to converge to the target controlled variable. Forexample, the air-fuel ratio correction coefficient KAF as the secondinput value may be calculated with an algorithm using a self tuningregulator, which is disclosed e.g. in Japanese Laid-Open PatentPublication (Kokai) No. 2006-2591. Further, as the algorithm forcalculating the air-fuel ratio correction coefficient KAF as the secondinput value, there may be used the control algorithm expressed by theaforementioned equations (39) to (47), or may be used the back-steppingcontrol algorithm, the PID control algorithm, the optimum controlalgorithm, the H^(∞) control algorithm, or the like.

Furthermore, although in the first embodiment, the correctionsensitivity Rlift is calculated using the response surface model formedby the maps shown in FIGS. 23 and 24, by way of example, the correctionsensitivity Rlift may be calculated using the response surface modelformed by the maps shown in FIGS. 21 and 22 in place of the responsesurface model formed by the maps shown in FIGS. 23 and 24. In short, thecorrection sensitivity Rlift may be calculated as a value equal to theerror weight W. Furthermore, if there is no need to avoid theovercompensation for the air-fuel ratio error estimated value Eaf by thelift correction value Dlift under the condition where the sensitivity ofthe air-fuel ratio error estimated value Eaf to the lift error is low,the equation (27) may be omitted to set Dlift to 1 in the equation (28).

Further, although in the first embodiment, the link weight functionsWcp_(i) are used as the plurality of predetermined functions, by way ofexample, the plurality of predetermined functions in the presentinvention are not limited to these, but any suitable functions may beused insofar as they are associated with a plurality of regions formedby dividing a region where a reference parameter is variable,respectively, and are set to values other than 0 only in the associatedregions while being set to 0 in regions other than the associatedregions, such that in regions overlapping each other, the absolute valueof the total sum of the values of functions associated with theoverlapping regions becomes equal to the absolute value of the maximumvalue of each function. For example, functions maximum values of whichare set to positive values or negative values other than 1 may be usedas the plurality of functions.

Further, as the plurality of functions, curved link weight functionsWcp_(i) using a sigmoid function, as shown in FIG. 39, may be used, forexample. In FIG. 39, NE×10 to Ne×16, which represent predeterminedvalues of the engine speed NE, are set to values which satisfy therelationship of NE×10<NE×11<NE×12<NE×13<NE×14<NE×15. When the regionwhere the engine speed NE is variable is divided into four regions of0≦NE<NE×11, 0<NE<NE×13, NE×11<NE<NE×15, and NE×13<NE≦NE×15, the fourlink weight functions Wcp_(i) are set such that they are associated withthe four regions, respectively, and are set to positive values notlarger than 1 in the regions associated therewith, whereas in regionsother than the associated regions, they are set to 0. Also when theabove link weight functions Wcp_(i) are used, it is possible to obtainthe same advantageous effects as provided by the FIG. 20 link weightfunctions Wcp_(i) according to the first embodiment.

Furthermore, although in the FIGS. 20 and 39, the values of the linkweight functions Wcp_(i) are set that they are associated with therespective regions of the engine speed NE, by way of example, the valuesof the link weight functions Wcp_(i) may be set such that they areassociated with a plurality of regions of the valve lift Liftin.

Further, although in the first embodiment, the engine speed NE and thevalve lift Liftin are used as reference parameters, by way of example,the reference parameters in the present invention are not limited tothese, but any suitable parameter may be used insofar as it is aparameter other than an controlled variable. For example, to control theair-fuel ratio of the engine 3 having the variable cam phase mechanism70, the cam phase Cain may be used as a reference parameter. Further, tocontrol the air-fuel ratio of the engine 3, which is not provided withthe variable valve lift mechanism 50 or the variable cam phase mechanism70 but with a throttle valve mechanism alone, the degree of opening ofthe throttle valve mechanism may be used as a reference parameter. Inaddition, in the case of a so-called speed-density engine, which isprovided with an intake pipe pressure sensor and a crank angle sensor,for controlling the air-fuel ratio based on parameters from the sensors,the intake pipe pressure and the engine speed NE may be used asreference parameters.

Next, a control apparatus 1A according to a second embodiment of thepresent invention will be described with reference to FIG. 40. Thecontrol apparatus 1A is distinguished from the control apparatus 1according to the first embodiment only in the configuration of themethod of calculating the lift correction value Dlift, and hereinafter,the description will be given of the different points. It should benoted that component elements of the control apparatus 1A, identical tothose of the control apparatus 1, are designated by identical referencenumerals, and detailed description thereof is omitted.

As shown in FIG. 40, the control apparatus 1A is equipped with anair-fuel ratio controller 100A in place of the air-fuel ratio controller100 according to the first embodiment. The air-fuel ratio controller100A is specifically implemented by the ECU 2, and includes a liftcorrection value-calculating section 130 in place of the lift correctionvalue-calculating section 120 of the air-fuel ratio controller 100according to the first embodiment. It should be noted that in thepresent embodiment, the air-fuel ratio controller 100A corresponds tothe control input-calculating means, and the lift correctionvalue-calculating section 130 corresponds to the model-modifying means.

As shown in FIG. 41, the lift correction value-calculating section 130is comprised of a link weight function-calculating section 131, an errorweight-calculating section 132, a transition coefficientweight-calculating section 133, a modified error-calculating section134, a basic local correction value-calculating section 135, acorrection sensitivity-calculating section 136, and a finalvalue-calculating section 137.

First, the link weight function-calculating section 131 calculates linkweight functions Wcp_(ij) by searching a map shown in FIG. 42 accordingto the engine speed NE and the valve lift Liftin. In this map, theregion of the engine speed NE and that of the valve lift Liftin areequally divided by I (I is an integer not smaller than 2) predeterminedvalues NE_(i) (i=1 to I) and J (J is an integer not smaller than 2)predetermined values Liftin_(j) (j=1 to J), respectively, and the linkweight functions Wcp_(ij) are set in a manner associated with aplurality of regions defined by combinations of three consecutive valuesof the engine speed NE and three consecutive values of the valve liftLiftin, respectively. It should be noted that in the present embodiment,the link weight functions Wcp_(ij) correspond to the plurality ofpredetermined functions.

Further, each of the link weight functions Wcp_(ij) takes the maximumvalue of 1 with respect to the values of the engine speed NE and thevalve lift Liftin in a center of each associated region, and in an areaother than the center, it takes a value which changes as on inclinedsurfaces of a square pyramid. Outside the regions, it takes 0. Inaddition, each adjacent two of a plurality of regions to whichcorrespond the link weight functions Wcp_(ij), respectively, overlapeach other, whereby the adjacent two of the link weight functionsWcp_(ij) intersect with each other, in respective portions where theychange as on inclined surfaces of a square pyramid.

For example, as shown in FIG. 43, a link weight function Wcp_(fg)corresponding to a region of NE_(f−1)<NE<NE_(f+1) andLiftin_(g−1)<Liftin<Liftin_(g+1) takes the maximum value of 1 when theengine speed NE and the valve lift Liftin are equal to values inrespective centers of the region, i.e. when NE=NE_(f) andLiftin=Liftin_(g) hold, but with respect to values NE and Liftin otherthan the values corresponding to the respective centers, the value ofthe link weight function Wcp_(fg) changes as on inclined surfaces of asquare pyramid. Now, f and g represent positive integers which satisfythe relationship of 0<f<0 and 0<g<j, respectively. Further, the linkweight function Wcp_(fg) is configured such that when the two values NEand Liftin are outside the above region, i.e. when NE≦NE_(f−1),NE_(f+1)≦NE, Liftin≦Liftin_(g−1) or Liftin_(g+1)≦Liftin holds, the linkweight function Wcp_(fg) takes 0.

Further, inclined surfaces of a square pyramid on which the value of thelink weight function Wcp_(fg) changes intersect with inclined surfacesof square pyramids on which change the respective values of the linkweight functions Wcp_(f−1g) and Wcp_(f+1g) corresponding to regionsadjacent to the region of the link weight function Wcp_(fg), in portionsof these regions where they overlap each other. Therefore, as shown inFIG. 43, assuming that NE_(x) is a value in the center between thevalues NE_(f) and NE_(f+1), e.g. when NE=NE_(x) and Liftin=Liftin_(g)hold, the values of the two link weight functions Wcp_(fg) andWcp_(f+1g) are such that Wcp_(fg)=Wcp_(f+1g)=0.5 holds, and all thevalues of the link weight functions Wcp_(ij) other than these becomeequal to 0. In addition, when NE_(x)<NE<NE_(f+1) and Liftin=Liftin_(g)hold, the value of the link weight function Wcp_(fg) becomes such that0<Wcp_(fg)<0.5 holds, while the value of the link weight functionWcp_(f+1g) becomes equal to (1−Wcp_(fg)), and all the values of theother link weight functions Wcp_(ij) other than these become equal to 0.

Further, as shown in FIG. 44, in overlapping portions of respectiveregions of the link weight function Wcp_(fg) and the link weightfunctions Wcp_(fg−1) and Wcp_(fg+1) adjacent thereto, i.e. portionswhere they change as on inclined surfaces, the inclined surfacesintersect with each other. Therefore, as shown in FIG. 44, assuming thatLiftin_(y) is a value in the center between Liftin_(g−1), andLiftin_(g), e.g. when NE=NE_(f) and Liftin=Liftin_(y) hold, the valuesof the two link weight functions Wcp_(fg−1) and Wcp_(fg) are such thatWcp_(fg−1)=Wcp_(fg)=0.5 holds, and the values of the other link weightfunctions Wcp_(ij) are all equal to 0. In addition, when NE=NE_(f) andLiftin_(y)<Liftin<Liftin_(g) hold, the value of the link weight functionWcp_(fg−1) becomes such that 0<Wcp_(fg−1)<0.5 holds, and the value ofthe link weight function Wcp_(fg) becomes equal to (1−Wcp_(fg−1)), butthe values of the other link weight functions Wcp_(ij) are all equal to0.

Although not shown, in overlapping portions of respective regions of thefunction Wcp_(fg) and the link weight functions Wcp_(f+1g−1) andWcp_(f−1g+1) adjacent thereto, i.e. portions where they change as oninclined surfaces, the inclined surfaces intersect with each other. Asdescribed above, in a square region defined by two adjacent values (e.g.NE_(f) and NE_(f+1)) of the engine speed NE and two adjacent values(e.g. Liftin_(g) and Liftin_(g+1)) of the valve lift Liftin, theinclined surfaces of the four link weight functions Wcp_(ij) (e.g.Wcp_(fg), Wcp_(fg+1), Wcp_(f+1g), and Wcp_(f+1g+1)) intersect with eachother, and the total sum of the four link weight functions Wcp_(ij) isset with respect to the values of the engine speed NE and the valve liftLiftin within the above region such that it becomes equal to 1. Itshould be noted that in the present embodiment, NE₁ and Liftin₁ shown inFIG. 42 are set to 0, respectively, and therefore, in actuality, in aregion of NE<NE₁ or Liftin<Liftin₁, the values of the link weightfunctions Wcp_(ij) are not set.

As described hereinabove, the link weight function-calculating section131 calculates the respective values of the link weight functionsWcp_(ij) by searching the map shown in FIG. 42 according to the enginespeed NE and the valve lift Liftin. That is, the link weight functionsWcp_(ij) are calculated as a matrix composed of the elements of I×Jvalues,

The error weight-calculating section 132 calculates the error weight Wby the same method as employed by the error weight-calculating section122. More specifically, the error weight W is calculated using searchvalues of the FIGS. 21 and 22 maps, described above, by theaforementioned equation (15). Further, the transition coefficientweight-calculating section 133 calculates the transition coefficientweight Wkg by the aforementioned equation (16), similarly to thetransition coefficient weight-calculating section 123.

Next, the modified error-calculating section 134 calculates a totalweight Wg_(ij) by the following equation (48), and then calculatesmodified errors Weaf_(ij) by the following equation (49).Wg _(ij)(k)=Wcp _(ij)(k)·W(k)·Wkg(k)  (48)Weaf _(ij)(k)=Wg _(ij)(k)·Eaf(k)  (49)

As described above, the modified errors Weaf_(ij) are calculated as amatrix composed of the elements of I×J values, and as values obtained byweighting the air-fuel ratio error estimated value Eaf by the threevalues Wcp_(ij), W, and Wkg. It should be noted in the presentembodiment, the modified errors Weaf_(ij) correspond to the plurality offirst multiplication values.

The basic local correction value-calculating section 135 calculatesbasic local correction values Dlift_bs_(ij) with a control algorithm towhich is applied a sliding mode control algorithm expressed by thefollowing equations (50) to (57). That is, the basic local correctionvalues Dlift_bs_(ij) are calculated as a matrix which is composed of theelements of I×J values, for causing the modified errors Weaf_(ij) toconverge to 0.σ_(ij)(k)=Weaf _(ij)(k)+S·Weaf _(ij)(k−1)  (50)Urch _(ij)(k)=−Krch·σ _(ij)(k)  (51)Unl _(ij)(k)=−Knl·sgn(σ_(ij)(k))  (52)Uadp _(ij)(k)=−Kadp·δ _(ij)(k)  (53)δ_(ij)(k)=λ·δ_(ij)(k−1)+σ_(ij)(k)  (54)When Dlift_(—) bs _(—) L<Dlift_(—) bs _(ij)(k−1)<Dlift_(—) bs _(—)Hλ=1  (55)When Dlift_(—) bs _(ij)(k−1)≦Dlift_(—) bs _(—) L or Dlift_(—) bs _(—)H≦Dlift_(—) bs _(ij)(k−1)λ=λlmt  (56)Dlift_(—) bs _(ij)(k)=Urch _(ij)(k)+Unl _(ij)(k)+Uadp _(ij)(k)  (57)

In the above equation (50), σ_(ij) represents a switching function, andS represents a switching function-setting parameter set to a value whichsatisfies the relationship of −1<S<0. In this case, the convergence rateof the modified errors Weaf_(ij) to 0 is designated by the value set tothe switching function-setting parameter S. Further, in the equation(51), Urch_(ij) represents a reaching law input, and Krch apredetermined reaching law gain. Furthermore, in the equation (52),Unl_(ij) represents a non-linear input, and Knl represents apredetermined non-linear input gain. Further, in the equation (52),sgn(σ_(ij)(k)) represents a sign function, and the value thereof is setsuch that sgn(σ_(ij)(k))=1 holds when σ_(ij)(k)≧0, and when σ_(ij)(k)<0,sgn(σ_(ij)(k))=−1 holds (it should be noted that the value thereof maybe set such that sgn(σ_(ij)(k))=0 holds when σ_(ij)(k)=0).

In the equation (53), Uadp_(ij) represents an adaptive law input, andKadp represents a predetermined adaptive law gain. Further, in theequation (53), δ_(ij) represents the integral value of a switchingfunction calculated by the equation (54). In the equation (54), λrepresents a forgetting coefficient, and as shown in the equations (55)and (56), the value thereof is set to 1 or a predetermined value λlmt,according to the results of comparisons between the immediatelypreceding value Dlift_bs_(ij)(k−1) of the basic local correction valueand predetermined upper and lower limit values Dlift_bs_H andDlift_bs_L.

Further, as shown in the equation (57), the basic local correction valueDlift_bs_(ij) is calculated as the sum of a reaching law inputUrch_(ij), a non-linear input Unl_(ij), and an adaptive law inputUadp_(ij). It should be noted that in the present embodiment, the basiclocal correction values Dlift_bs_(ij) correspond to the plurality ofmodification values.

The forgetting coefficient λ is used in the algorithm for calculatingthe basic local correction values Dlift_bs_(ij) because, as describedabove, the adaptive law inputs Uadp′ and Uadp_(ij) as integral terms inthe two control algorithms are prevented from interfering with eachother to prevent them from exhibiting oscillating behaviors, and theabsolute values of the respective adaptive law inputs are prevented frombeing very large, to thereby prevent improper modification of thecorrelation model so as to improve controllability in a transient state.Further, when the immediately preceding value Dlift_bs_(ij)(k−1) of thebasic local correction value is within the aforementioned range, asdescribed above, the forgetting coefficient λ is set to 1 so as tocancel the forgetting effect provided by the forgetting coefficient λ.It should be noted that when the forgetting effect by the forgettingcoefficient λ is always unnecessary, the forgetting coefficient λ areonly required to 1 in the equation (54) irrespective of the magnitude ofthe immediately preceding value Dlift_bs_(ij)(k−1).

On the other hand, the above-described correctionsensitivity-calculating section 136 calculates the correctionsensitivity Rlift by the same method as employed by the correctionsensitivity-calculating section 126. More specifically, the correctionsensitivity Rlift is calculated using the values retrieved from theFIGS. 23 and 24 maps, described above, by the aforementioned equation(27).

Then, the final value-calculating section 137 calculates localcorrection values Dlift_lc_(ij) by the following equation (59), and thenfinally calculates the lift correction value Dlift by the followingequation (59). It should be noted that in the present embodiment, thelocal correction values Dlift_lc_(ij) correspond to the plurality ofsecond multiplication values, and the plurality of multiplicationvalues.

$\begin{matrix}{{{Dlift\_ lc}_{ij}(k)} = {{{{Rlift}(k)} \cdot {Wcp}_{ij} \cdot {Dlift\_ bs}_{ij}}(k)}} & (58) \\{{{Dlift}(k)} = {\sum\limits_{i = 1}^{I}{\sum\limits_{j = 1}^{J}{{Dlift\_ lc}_{ij}(k)}}}} & (59)\end{matrix}$

As described above, the lift correction value-calculating section 130calculates the lift correction value Dlift as the total sum of the localcorrection values Dlift_lc_(ij) obtained by multiplying the basic localcorrection values Dlift_bs_(ij) by the correction sensitivity Rlift andthe link weight functions Wcp_(ij). In this case, since the basic localcorrection values Dlift_bs_(ij) are values for causing the modifiederrors Weaf_(ij) to converge to 0, the correction of the valve liftLiftin using the lift correction value Dlift corresponds correcting ormodifying the valve lift Liftin such that the lift error is eliminated.For this reason, the calculation of the basic estimated intake airamount Gcyl_vt_base by searching the aforementioned FIG. 43 mapaccording to the corrected valve lift Liftin_mod thus calculatedcorresponds to calculating the first estimated intake air amount Gcyl_vtas the first input value by using a map modified such that the lifterror is eliminated, that is, a correlation model.

As described hereinabove, according to the control apparatus 1A of thesecond embodiment, the lift correction value Dlift is calculated usingthe link weight functions Wcp_(ij) in place of the link weight functionsWcp_(i) according to the first embodiment, and hence it is possible toobtain the same advantageous effects as provided by the controlapparatus 1 of the first embodiment. In addition thereto, since the linkweight functions Wcp_(ij) are calculated based on the valve lift Liftinand the engine speed NE, it is possible to properly compensate for achange in the lift error in each region defined by the valve lift Liftinand the engine speed NE. Particularly even if deviation of thecorrelation model from the actual correlation of the valve lift Liftinand the engine speed NE with the basic estimated intake air amountGcyl_vt_base is different between the I×J regions of the valve liftLiftin and the engine speed NE in the direction of change in thedeviation, it is possible to properly modify the correlation model on anregion-by-region basis while coping with the deviation. This makes itpossible, compared with the first embodiment which uses the link weightfunctions Wcp_(i) calculated based on the engine speed NE alone, toenhance the accuracy and stability of control.

It should be noted that although in the second embodiment, the controlalgorithm expressed by the aforementioned equations (50) to (57) is usedfor the algorithm for calculating the basic local correction valueDlift_bs_(ij), by way of example, this is not limitative, but the basiclocal correction value Dlift_bs_(ij) may be calculated with a controlalgorithm expressed by the following equations (60) to (68), to whichare applied a combination of an adaptive disturbance observer and asliding mode control algorithm.

$\begin{matrix}{{\sigma_{ij}(k)} = {{{Weaf}_{ij}(k)} + {S \cdot {{Weaf}_{ij}\left( {k - 1} \right)}}}} & (60) \\{{{Urch}_{ij}(k)} = {{- {Krch}} \cdot {\sigma_{ij}(k)}}} & (61) \\{{{Unl}_{ij}(k)} = {{- {Knl}} \cdot {{sgn}\left( {\sigma_{ij}(k)} \right)}}} & (62) \\{{\sigma_{ij}{\_ hat}(k)} = {{{Urch}_{ij}\left( {k - 1} \right)} + {{Unl}_{ij}\left( {k - 1} \right)} + {{Uls}_{ij}\left( {k - 1} \right)}}} & (63) \\\begin{matrix}{{{E\_ sig}_{ij}(k)} = {{\sigma_{ij}(k)} - {\sigma_{ij}{\_ hat}(k)}}} \\{= {{\sigma_{ij}(k)} - {{Urch}_{ij}\left( {k - 1} \right)} - {{Unl}_{ij}\left( {k - 1} \right)} - {{Uls}_{ij}\left( {k - 1} \right)}}}\end{matrix} & (64) \\{{{Uls}_{ij}(k)} = {{\lambda \cdot {{Uls}_{ij}\left( {k - 1} \right)}} + {\frac{P}{1 + P}{E\_ sig}_{ij}(k)}}} & (65) \\{{{*{When}\mspace{14mu}{Dlift\_ bs}{\_ L}} < {{Dlift\_ bs}_{ij}\left( {k - 1} \right)} < {{Dlift\_ bs}{\_ H}}}{\lambda = 1}} & (66) \\{{{*{When}\mspace{14mu}{Dlift\_ bs}_{ij}\left( {k - 1} \right)} \leqq {{Dlift\_ bs}{\_ L}\mspace{14mu}{or}\mspace{14mu}{Dlift\_ bs}{\_ H}} \leqq {{Dlift\_ bs}_{ij}\left( {k - 1} \right)}}{\lambda = {\lambda\;{lmt}}}} & (67) \\{{{Dlift\_ bs}_{ij}(k)} = {{{Urch}_{ij}(k)} + {{Unl}_{ij}(k)} + {{Uls}_{ij}(k)}}} & (68)\end{matrix}$

In the above equation (63), σ_(ij) _(—) hat represents an estimatedvalue of a switching function, and Uls_(ij) represents a disturbanceestimated value. The disturbance estimated value Uls_(ij) is calculatedwith a fixed gain identification algorithm expressed by the equations(64) and (65). In the equation (64), E_sig_(ij) represents an estimationerror. In the equation (65), P represents a fixed identification gain.It should be noted that the above equations (63) to (67) express analgorithm for calculating the disturbance estimated value Uls_(ij) ofthe adaptive disturbance observer.

In the equation (65), the immediately preceding value Uls_(ij)(k−1) ofthe disturbance estimated value is multiplied by the forgettingcoefficient λ, and if the absolute value of the basic local correctionvalue Dlift_bs_(ij) is large, the forgetting coefficient λ is set to avalue within the range of 0<λ<1. Therefore, the aforementionedforgetting effect makes it possible to prevent the integral terms Uadp′and Uadp_(ij) in the respective control algorithms for calculating theair-fuel ratio correction coefficient KAF and the basic local correctionvalues Dlift_bs_(ij) from interfering with each other to thereby preventthe integral terms from exhibiting oscillating behaviors, and theabsolute values of the respective integral terms from becoming verylarge. This makes it possible to avoid improper modification of thecorrelation model. As a result, the calculation accuracy of the firstestimated intake air amount Gcyl_vt can be enhanced, thereby making itpossible to improve controllability in a transient state. Further, ifthe absolute value of the immediately preceding value Dlift_bs_(ij)(k−1)of the basic local correction value is small, the forgetting coefficientλ is set to 1, and hence even when the modified error Weaf_(ij) becomesclose to 0, the basic local correction values Dlift_bs_(ij) can be heldat proper values. This makes it possible to enhance the responsivenessof the air-fuel ratio control when the modified errors Weaf_(ij) startto increase, thereby making it possible to enhance the control accuracy.

In addition to the above, since the disturbance estimated value Uls_(ij)is calculated with the fixed gain identification algorithm of theadaptive disturbance observer, compared with the control algorithmaccording to the second embodiment that uses the adaptive law inputUadp_(ij), it is possible to further enhance the capability ofsuppressing the integral fluctuation behavior and the overshootingbehavior of the basic local correction values Dlift_bs_(ij).

Further, although in the second embodiment, the engine speed NE and thevalve lift Liftin are used as reference parameters, by way of example,the reference parameters according to the present invention are notlimited to these, but any suitable parameter may be used insofar as itis a parameter other than an controlled variable. For example, tocontrol the air-fuel ratio of the engine 3 having the variable cam phasemechanism 70, the cam phase Cain may be used as a reference parameter inaddition to the engine speed NE and the valve lift Liftin. Further, tocontrol the air-fuel ratio of the engine 3, which is not provided withthe variable valve lift mechanism 50 or the variable cam phase mechanism70 but with a throttle valve mechanism alone, the degree of opening ofthe throttle valve mechanism may be used as a reference parameter. Inaddition, in the case of the so-called speed-density engine, which isprovided with an intake pipe pressure sensor and a crank angle sensor,for controlling the air-fuel ratio based on parameters from the sensors,the intake pipe pressure and the engine speed NE may be used asreference parameters.

Furthermore, although in the second embodiment, the valve lift Liftin isused as an operating state parameter indicative of the operating statesof the variable intake mechanism, by way of example, the operating stateparameter in the control apparatus according to the present invention isnot limited to this. For example, to control the air-fuel ratio of theengine 3 having the variable cam phase mechanism 70, the cam phase Cainmay be used as an operating state parameter. Further, to control theair-fuel ratio of the engine 3, which is not provided with the variablevalve lift mechanism 50 or the variable cam phase mechanism 70 but witha throttle valve mechanism alone, the degree of opening of the throttlevalve mechanism may be used as an operating state parameter. Inaddition, in the case of the so-called speed-density engine, which isprovided with an intake pipe pressure sensor and a crank angle sensor,for controlling the air-fuel ratio based on parameters from the sensors,the intake pipe pressure and the engine speed NE may be used asoperating state parameters.

On the other hand, although in the second embodiment, the link weightfunction-calculating section 131 uses the FIG. 42 map as a map forcalculating the link weight functions Wcp_(ij), the link weightfunction-calculating section 131 may use maps in which the values of thelink weight functions Wcp_(ij) are set according to the second correctedvalve lift Liftin_mod_p and the engine speed NE, as maps for usecalculating the link weight functions Wcp_(ij). In short, in FIG. 42, amap may be used in which the values of the link weight functionsWcp_(ij) are set according to the second corrected valve liftLiftin_mod_p in place of the valve lift Liftin.

Further, although in the second embodiment, the link weight functionsWcp_(ij) are used as the plurality of predetermined functions, by way ofexample, the plurality of predetermined functions in the presentinvention are not limited to these, but any suitable functions may beused insofar as they are associated with a plurality of regions formedby dividing a region where a reference parameter is variable,respectively, and set to values other than 0 only in the associatedregions while being set to 0 in regions other than the associatedregions, such that in regions overlapping each other, the absolute valueof the total sum of the values of functions associated with theoverlapping regions becomes equal to the absolute value of the maximumvalue of each function. For example, functions maximum values of whichare set to positive values or negative values other than 1 may be usedas the plurality of functions.

Next, a control apparatus 1B (see FIG. 45) according to a thirdembodiment of the present invention will be described. It should benoted that in the following description, component elements of thecontrol apparatus 1B, identical to those of the control apparatus 1according to the first embodiment, are designated by identical referencenumerals, and detailed description thereof is omitted. The controlapparatus 1B is applied to a vehicle of a so-called FR system, notshown, which has the engine 3 with the aforementioned automatictransmission installed on a front side thereof, and includes rear wheelsand front wheels, neither of which is shown, as drive wheels andnon-drive wheels, respectively. More specifically, the control apparatus1B is provided for carrying out traction control of the vehicle.

It should be noted that the term “traction control” is intended to meana control method of reducing engine torque, when the engine torquebecomes too large during acceleration of the vehicle, thereby causing astate in which the drive wheels rotate without load or idle with respectto the non-drive wheels, so as to avoid the idling state to therebyensure the stability of the vehicle to enhance the accelerationperformance of the engine 3.

Referring to FIG. 45, the control apparatus 1B includes the ECU 2. Tothe ECU 2 are connected not only the aforementioned sensors 20 to 27 butalso left and right front wheel speed sensors 80 and 81, and left andright rear wheel speed sensors 82 and 83. The left and right front wheelspeed sensors 80 and 81 detect the speeds of the left and right frontwheels, to deliver signals indicative of the respective sensed left andlight front wheel speeds to the ECU 2. The left and right rear wheelspeed sensors 82 and 83 detect the speeds of the left and right rearwheels, to deliver signals indicative of the respective sensed left andright rear wheel speeds to the ECU 2.

The ECU 2 calculates the left and right front wheel speeds based on thesignals from the left and right front wheel speed sensors 80 and 81, andcalculates the arithmetic mean thereof as a non-drive wheel speedWs_ref. Further, the ECU 2 calculates the left and right rear wheelspeeds based on the signals from the left and right rear wheel speedsensors 82 and 83, and calculates the arithmetic mean thereof as a drivewheel speed Ws_act. It should be noted that in the present embodiment,the left and right front wheel speed sensors 80 and 81 correspond to thereference parameter-detecting means, the non-drive wheel speed Ws_refcorresponds to the reference parameter and a second wheel speed, whilethe left and right rear wheel speed sensors 82 and 83 correspond to thecontrolled variable-detecting means, and the drive wheel speed Ws_actcorresponds to the controlled variable and a first wheel speed.

Further, as shown in FIG. 46, the control apparatus 1B includes atraction controller 200. As described hereinafter, the tractioncontroller 200 is provided for calculating the engine torque Trq astorque of the engine 3 which makes it possible to avoid the idling stateof the drive wheels, to thereby ensure the stability of the vehicle andenhance the acceleration performance of the engine 3 in a compatiblemanner. The traction controller 200 is implemented by the ECU 2. Itshould be noted that in the present embodiment, the traction controller200 corresponds to the control input-calculating means, and the enginetorque Trq corresponds to the control input and the output of the engine3.

As shown in FIG. 46, the traction controller 200 is comprised of atarget wheel speed-calculating section 201, a wheel speed feedbackcontroller 202, a maximum/minimum torque-calculating section 203, anormalization demand driving force-calculating section 204, amultiplication element 205, a feedforward torque-calculating section206, an addition element 207, and a torque correction value-calculatingsection 210.

First, the target wheel speed-calculating section 201 calculates atarget wheel speed Ws_cmd by the following equation (69). It should benoted that in the present embodiment, the target wheel speed-calculatingsection 201 corresponds to target controlled variable-setting means, andthe target wheel speed Ws_cmd corresponds to the target controlledvariable.Ws _(—) cmd(k)=Ws _(—) ref(k)+OptSlip  (69)

In the above equation (69), OptSlip represents a predetermined slipoffset value which corresponds to a slip amount allowable between thedrive wheels and the non-drive wheels, and in the present embodiment, itis set to a fixed value (e.g. 10 km/h). It should be noted that the slipoffset value OptSlip may be determined by searching a map or apredetermined equation, according to a predetermined parameter (e.g. thenon-drive wheel speed Ws_ref, an estimated value of the frictionalresistance coefficient of a road surface, a detection signal from a yawrate sensor, a detection signal from a slip angle sensor mounted on thebody of the vehicle, etc.).

Further, the wheel speed feedback controller 202 calculates a torquefeedback value Trq_fb by a method, described hereinafter, based on thetarget wheel speed Ws_cmd and the drive wheel speed Ws_act. It should benoted that in the present embodiment, the wheel speed feedbackcontroller 202 corresponds to the error parameter-calculating means, andthe torque feedback value Trq_fb corresponds to the error parameter andthe second input value.

Furthermore, the torque correction value-calculating section 210calculates a torque correction value Ktrq by a method, describedhereinafter, based on the torque feedback value Trq_fb, the engine speedNE, and the non-drive wheel speed Ws_ref. It should be noted that in thepresent embodiment, the torque correction value-calculating section 210corresponds to the model-modifying means.

On the other hand, the maximum/minimum torque-calculating section 203calculates a maximum torque Trq_max and a minimum torque Trq_min bysearching a map shown in FIG. 47 according to the engine speed NE. InFIG. 47, NEhigh represents a predetermined maximum allowable enginespeed (e.g. 7000 rpm). These values Trq_max and Trq_min represent themaximum value and the minimum value of the engine torque which can beachieved when the engine speed NE is equal to the associated enginespeed. Further, in this map, the minimum torque Trq_min is set to anegative value. This is because the minimum torque Trq_min correspondsto engine torque obtained in a state in which the accelerator pedal isnot stepped on, i.e. in an engine brake state during a deceleration fuelcut-off operation.

It should be noted that in the present embodiment, the crank anglesensor 20 and the maximum/minimum torque-calculating section 203correspond to the reference parameter-detecting means, and the minimumtorque Trq_min corresponds to the reference parameter and a limit valueof the output of the engine 3.

Further, the normalization demand driving force-calculating section 204calculates a normalization demand driving force Ktrq_ap by searching amap shown in FIG. 48 according to the accelerator pedal opening AP. InFIG. 48, APmax represents the maximum value (100%) of the acceleratorpedal opening. Further, the normalization demand driving force Ktrq_aprepresents a value obtained by normalizing the normalization demanddriving force Ktrq_ap determined based on the accelerator pedal openingAP, with reference to a demand driving force Trq_apmax obtained whenAP=APmax holds, that is, a value which satisfies the equation,Ktrq_ap=Trq_ap÷Ktrq_apmax.

The multiplication element 205 calculates a corrected maximum torqueTrq_max_mod by the following equation (70). More specifically, thecorrected maximum torque Trq_max_mod is calculated by correcting themaximum torque Trq_max by the torque correction value Ktrq.Trq_max_mod(k)=Ktrq(k)·Trq_max(k)  (70)

Further, the feedforward torque-calculating section 206 calculates afeedforward torque Trq_ff by the following equation (71).Trq _(—) ff(k)=Ktrq _(—)ap(k){Trq_max_mod(k)−Ttrq_min(k)}+Ttrq_min(k)  (71)

It should be noted that in the present embodiment, the feedforwardtorque-calculating section 206 corresponds to the first inputvalue-calculating means, and the feedforward torque Trq_ff correspondsto the first input value. Further, calculating the feedforward torqueTrq_ff using the equations (70) and (71) corresponds to calculating thefirst input value using a modified correlation model.

Then, finally, the addition element 207 calculates the engine torque Trqby the following equation (72). More specifically, the engine torque Trqis calculated as the sum of the torque feedback value Trq_fb and thefeedforward torque Trq_ff.Trq(k)=Trq _(—) fb(k)+Trq _(—) ff(k)  (72)

Next, a description will be given of the aforementioned wheel speedfeedback controller 202. The wheel speed feedback controller 202calculates the torque feedback value Trq_fb with a control algorithmexpressed by the following equations (73) to (78), to which are applieda combination of a target value filter-type two-degree-of-freedomsliding mode control algorithm, and an adaptive disturbance observer.

$\begin{matrix}{{{Ws\_ cmd}{\_ f}(k)} = {{{{- {Rt}} \cdot {Ws\_ cmd}}{\_ f}\left( {k - 1} \right)} + {\left( {1 + {Rt}} \right){Ws\_ cmd}(k)}}} & (73) \\{{{Et}(k)} = {{{Ws\_ act}(k)} - {{Ws\_ cmd}{\_ f}(k)}}} & (74) \\{{\sigma\;{t(k)}} = {{{Et}(k)} + {{St} \cdot {{Et}\left( {k - 1} \right)}}}} & (75) \\{{{Urch\_ t}(k)} = {{{- {Krch\_ t}} \cdot \sigma}\;{t(k)}}} & (76) \\{{{Unl\_ t}(k)} = {{- {Knl\_ t}} \cdot {{sgn}\left( {\sigma\;{t(k)}} \right)}}} & (77) \\{{\sigma\;{t\_ hat}(k)} = {{{Urch\_ t}\left( {k - 1} \right)} + {{Unl\_ t}\left( {k - 1} \right)} + {{Uls\_ t}\left( {k - 1} \right)}}} & (78) \\\begin{matrix}{{{Et\_ sig}(k)} = {{\sigma\;{t(k)}} - {\sigma\;{t\_ hat}(k)}}} \\{= {{\sigma\;{t(k)}} - {{Urch\_ t}\left( {k - 1} \right)} - {{Un\_ t}\left( {k - 1} \right)} - {{Uls\_ t}\left( {k - 1} \right)}}}\end{matrix} & (79) \\{{{Uls\_ t}(k)} = {{\lambda\;{t \cdot {Uls\_ t}}\left( {k - 1} \right)} + {\frac{Pt}{1 + {Pt}}{Et\_ sig}(k)}}} & (80) \\{{{*{When}\mspace{14mu}{Uls\_ t}{\_ L}} < {{Uls\_ t}\left( {k - 1} \right)} < {{Uls\_ t}{\_ H}}}{{\lambda\; t} = 1}} & (81) \\{{{*{When}\mspace{14mu}{Uls\_ t}\left( {k - 1} \right)} \leqq {{Uls\_ t}{\_ L}\mspace{14mu}{or}\mspace{14mu}{Uls\_ t}{\_ H}} \leqq {{Uls\_ t}\left( {k - 1} \right)}}{{\lambda\; t} = {\lambda\;{tlmt}}}} & (82) \\{{{Trq\_ fb}(k)} = {{{Urch\_ t}(k)} + {{Unl\_ t}(k)} + {{Uls\_ t}(k)}}} & (83)\end{matrix}$

In the above control algorithm, first, a filtered value Ws_cmd_f of thetarget wheel speed is calculated with a first order lag type low passfilter algorithm expressed by the equation (73). In the equation (73),Rt represents a target value filter-setting parameter, and is et to avalue which satisfies the relationship of −1<Rt<0. In this case, thefollow-up speed of the filtered value Ws_cmd_f to the target wheel speedWs_cmd is determined by a value set to the target value filter-settingparameter Rt.

Then, a reaching law input Urch_t and a non-linear input Unl_t arecalculated with a control algorithm to which is applied a sliding modecontrol algorithm expressed by the following equations (74) to (77). Inthe equation (74), Et represents a follow-up error, and in the equation(75), σt represents a switching function. Further, in the equation (75),St represents a switching function-setting parameter, and is set to avalue which satisfies the relationship pf−1<St<0. In this case, theconvergence rate of the follow-up error Et to 0 is designated by a valueset to the switching function-setting parameter St. Further, in theequation (76), Krch_t represents a predetermined reaching law gain, andin the equation (77), Knl_t represents a predetermined non-linear inputgain. Furthermore, in the equation (77), sgn(σt(k)) represents a signfunction, and the value thereof is set such that sgn(σt(k))=1 holds whenσt(k)≧0, and when σt(k)<0, sgn(σt(k))=−1 holds (it should be noted thatthe value thereof may be set such that sgn(σt(k))=0 holds when σt(k)=0).

Then, a disturbance estimated value Uls_t is calculated with a controlalgorithm to which is applied an adaptive disturbance observer expressedby the equations (78) to (82). In the equation (78), σt_hat representsan estimated value of a switching function, and Uls_t represents adisturbance estimated value. The disturbance estimated value Uls_t iscalculated with a fixed gain identification algorithm expressed by theequations (79) and (80). In the equation (79), Et_sig represents anestimation error, and in the equation (80), Pt represents a fixedidentification gain.

Further, in the equation (80), λt represents a forgetting coefficient,and as shown in the equations (81) and (82), the value thereof is set to1 or a predetermined value λtlmt, according to the results ofcomparisons between the immediately preceding value Uls_t(k−1) of thedisturbance estimated value and predetermined upper and lower limitvalues Uls_t_H and Uls_t_L. The upper limit value Uls_t_H is set to apredetermined positive value, and the lower limit value Uls_t_L is setto a predetermined negative value, while the predetermined value λtlmtis set a value which satisfies the relationship of 0<λtlmt<1.

Then, as shown in the equation (83), the torque feedback value Trq_fb isfinally calculated as the sum of the reaching law input Urch_t, thenon-linear input Unl_t, and the disturbance estimated value Uls_t.

As described above, the wheel speed feedback controller 202 calculatesthe torque feedback value Trq_fb with the control algorithm expressed bythe equations (73) to (78), and therefore the torque feedback valueTrq_fb is calculated as a value for causing the drive wheel speed Ws_actto converge to the filtered value Ws_cmd_f of the target wheel speed, inother words, as a value for causing the drive wheel speed Ws_act toconverge to the target wheel speed Ws_cmd. In this case, as describedhereinabove, the target wheel speed Ws_cmd is calculated by adding theslip offset value OptSlip to the non-drive wheel speed Ws_ref, so thatin a state of Ws_act≈Ws_cmd, Ws_ref−Ws_act≈OptSlip holds.

Further, the torque feedback value Trq_fb is calculated using theforgetting coefficient λt, and hence if the absolute value of theimmediately preceding value Uls_t(k−1) of the disturbance estimatedvalue is large, the above-described forgetting effect makes it possibleto prevent the disturbance estimated value Uls_t, i.e. the torquefeedback value Trq_fb from being integrally increased, whereby it ispossible to ensure the stability of the responsiveness of the controlsystem in a transient state. Further, if the absolute value of theimmediately preceding value Uls_t(k−1) of the disturbance estimatedvalue is small, the forgetting coefficient λt is set to 1, and henceeven when the follow-up error Et has converged to 0, the torque feedbackvalue Trq_fb can be held at a value appropriate enough to compensate forthe follow-up error Et quickly, whereby it is possible to enhance theresponsiveness when the follow-up error Et starts to increase.

Next, the aforementioned torque correction value-calculating section 210will be described with reference to FIG. 49. As described hereinafter,the torque correction value-calculating section 210 is provided forcalculating the torque correction value Ktrq for use in correcting themaximum torque Trq_max such that a torque error Etf, which is regardedas a control error to be compensated for, becomes equal to 0. As shownin FIG. 49, the torque correction value-calculating section 210 iscomprised of a link weight function-calculating section 211, an errorweight-calculating section 212, a torque error-calculating section 213,a modified torque error-calculating section 214, a basic localcorrection value-calculating section 215, a torque correctionsensitivity-calculating section 216, and a final value-calculatingsection 217.

First, the link weight function-calculating section 211 calculates linkweight functions Wcv_(i) by searching a map shown in FIG. 50 accordingto the engine speed NE. It should be noted that in the presentembodiment, the link weight functions Wcv_(i) correspond to a pluralityof predetermined functions. In this map, the values of the link weightfunctions Wcv_(i) are set similarly to the above-described link weightfunctions Wcp_(i). That is, the link weight function Wcv_(i) iscalculated as a vector which is composed of the elements of four values.

When a region within which the engine speed NE is variable is dividedinto four regions of 0≦NE<NE×3, NE×1<NE<NE×5, NE×3<NE<NE×7, andNE×5<NE≦NE×8, the values of the above four link weight functions Wcv_(i)are set such that they are associated with the four regions,respectively, and set to positive values not larger than 1 in theregions associated therewith, whereas in regions other than theassociated regions, they are set to 0.

It should be noted that link weight functions Wcv_(i) composed of theelements of two or three values or five or more values may be used inplace of the FIG. 50 link weight functions Wcp_(i) composed of theelements of four values. In this case, the regions of the engine speedNE are only required to be set such that they overlap each other,according the number of the elements.

The error weight-calculating section 212 calculates a error weight Wt bysearching a map shown in FIG. 51 according to the engine speed NE andthe non-drive wheel speed Ws_ref. The error weight Wt takes a valueobtained by normalizing a ratio ΔWs_act/ΔTrq between the amount ΔWs_actof change in the drive wheel speed Ws_act and the amount ΔTrq of changein the engine torque, with reference to the absolute value|ΔWs_act_ref/ΔTrq_ref| of a ratio ΔWs_act_ref/ΔTrq_ref obtained at apredetermined drive wheel speed and a predetermined engine torque, thatis, a value which satisfies the equation,Wt=(ΔWs_act/ΔTrq)÷(|ΔWs_act_ref/ΔTrq_ref|).

The error weight Wt represents a probability of the torque error Etfbeing caused by a too large amount of the engine torque Trq, when it isassumed that the correlation between the engine speed NE and thefeedforward torque Trq_ff, that is, the correlation between the maximumtorque Trq_max and the feedforward torque Trq_ff is changed by a suddenincrease in the accelerator pedal opening AP, whereby the torque errorEtf, i.e. the slippage of a drive wheel is caused. More specifically,the error weight Wt is set to a larger value as the probability of thetorque error Etf being caused by a too large amount of the engine torqueTrq is higher. In other words, the error weight Wt is calculated as avalue which represents the degree of influence of the maximum torqueTrq_max on the torque error Etf. Further, since the degree of theinfluence of the maximum torque Trq_max on the torque error Etf alsovaries with the gear ratio of the transmission, in FIG. 51, the errorweight Wt is set according to the engine speed NE and the non-drivewheel speed Ws_ref.

In FIG. 51, Ws_ref 1 to Ws_ref 3 represent predetermined values of thenon-drive wheel speed, which satisfy the relationship of Ws_ref 1<Ws_ref2<Ws_ref 3. In this map, the error weight Wt is set to a smaller valueas the non-drive wheel speed Ws_ref is higher. This is because when thenon-drive wheel speed Ws_ref is high, the slippage of a drive wheel ismore difficult to occur as the gear ratio of the transmission is higher,and hence the error weight Wt is set to a smaller value to thereby makesmaller the amount of correction of the maximum torque Trq_max by thetorque correction value Ktrq in the decreasing direction. Further, theerror weight Wt is set such that it has the same tendency with respectto the engine speed NE as a torque curve in engine performance curveshas. This is because the error weight Wt is a value indicative of thedegree of influence of the maximum torque Trq_max on the torque errorEtf.

Further, the torque error-calculating section 213 calculates the torqueerror Etf by the following equation (84):Etf(k)=Trq _(—) fb(k)−Trq _(—) fb _(—) cmd(k)  (84)

In the above equation (84), Trq_fb_cmd represents a target torquefeedback value serving as a target of a torque feedback value Trq_fb,and is set to a fixed value (e.g. 0). It should be noted that in thepresent embodiment, the target torque feedback value Trq_fb_cmdcorresponds to a predetermined target value, and the torque error Etfcorresponds to the difference between the error parameter and thepredetermined target value.

Then, the modified torque error-calculating section 214 calculatesmodified torque errors Wetrq_(i) by the following equation (85). Morespecifically, the modified torque error Wetrq_(i) is calculated as avector which is composed of the elements of four values. It should benoted that in the present embodiment, the modified torque errorsWetrq_(i) correspond to the plurality of first multiplication values.Wetrq _(i)(k)=Wt(k)·Wcv _(i)(k)·Etf(k)  (85)

Next, the basic local correction value-calculating section 215calculates basic local correction values Dktrq_bs_(i) with a controlalgorithm to which is applied a sliding mode control algorithm expressedby the following equations (86) to (93). That is, the basic localcorrection value Dktrq_bs_(i) is calculated as a vector which iscomposed of the elements of four values. It should be noted that in thepresent embodiment, the basic local correction values Dktrq_bs_(i)correspond to the plurality of modification values.σv _(i)(k)=Wetrq _(i)(k)+Sv·Wetrq _(i)(k−1)  (86)Urch _(—) v _(i)(k)=−Krch _(—) v·σv _(i)(k)  (87)Unl _(—) v _(i)(k)=−Knl _(—) v·sgn(σv _(i)(k))  (88)Uadp _(—) v _(i)(k)=−Kadp _(—) v·δv _(i)(k)+Uadp _(—) v _(—) ini  (89)δv _(i)(k)=λv·δv _(i)(k−1)+σv _(i)(k)  (90)When Dktrq _(—) bs _(—) L<Dktrq _(—) bs _(i)(k−1)<Dktrq _(—) bs _(—)Hλv=1  (91)When Dktrq _(—) bs _(i)(k−1)≦Dktrq _(—) bs _(—) L or Dktrq _(—) bs _(—)H≦Dktrq _(—) bs _(i)(k−1)λv=λvlmt  (92)Dktrq _(—) bs _(i)(k)=Urch _(—) v _(i)(k)+Unl _(—) v _(i)(k)+Uadp _(—) v_(i)(k)  (93)

In the above equation (86), σv_(i) represents a switching function, andSv a switching function-setting parameter which is set to a valuesatisfying the relationship of −1<Sv<St<0. The reason for thus settingthe two switching function-setting parameters St and Sv will bedescribed hereinafter. In this case, the convergence rate of themodified torque errors Wetrq_(i) to 0 is designated by a value set tothe switching function-setting parameter Sv. Further, in the equation(87), Urch_v_(i) represents a reaching law input, and Krch_v representsa predetermined reaching law gain. Furthermore, in the equation (88),Unl_v_(i) represents a non-linear input, and Knl_v represents apredetermined non-linear input gain. Further, in the equation (88),sgn(σv_(i)(k)) represents a sign function, and the value thereof is setsuch that sgn(σv_(i)(k))=1 holds when σv_(i)(k)≧0, and when σv_(i)(k)<0,sgn(σv_(i)(k))=−1 holds (it should be noted that the value thereof maybe set such that sgn(σv_(i)(k))=0 holds when σv_(i)(k)=0).

In the equation (89), Uadp_v_(i) represents an adaptive law input, andKadp_v represents a predetermined adaptive law gain. Further, in theequation (89), Uadp_v_ini represents the initial value of the adaptivelaw input, and is set to a fixed value (e.g. 1). Furthermore, in theequation (89), δv_(i) represents the integral value of a switchingfunction calculated by the equation (90). In the equation (90), vrepresents a forgetting coefficient, and as shown in the equations (91)and (92), the value thereof is set to 1 or a predetermined value λvlmt,according to the results of comparisons between the immediatelypreceding value Dktrq_bs_(i)(k−1) of the basic local correction valueand predetermined upper and lower limit values Dktrq_bs_H andDktrq_bs_L. The upper limit value Dktrq_bs_H is set to a predeterminedpositive value, and the lower limit value Dktrq_bs_L is set to apredetermined negative value, while the predetermined value λvlmt is seta value which satisfies the relationship of 0<λvlmt<1.

Further, as shown in the equation (93), the basic local correction valueDktrq_bs_(i) is calculated as the sum of the reaching law inputUrch_v_(i), the non-linear input Unl_v_(i), and the adaptive law inputUadp_v_(i).

As described above, the basic local correction value-calculating section215 calculates the basic local correction values Dktrq_bs_(i) with thecontrol algorithm expressed by the following equations (86) to (93), andtherefore the basic local correction values Dktrq_bs_(i) are calculatedas values for causing the modified torque errors Wetrq_(i) to convergeto 0, respectively, in other words, as values for causing the torquefeedback value Trq_fb to converge to the target torque feedback valueTrq_fb_cmd.

Further, the basic local correction values Dktrq_bs_(i) are calculatedusing the forgetting coefficient λv, and hence when the absolute valueof the immediately preceding value Dktrq_bs_(i)(k−1) of the basic localcorrection value is large, the aforementioned forgetting effect makes itpossible to prevent the integral terms Uls_t and Uadp_v_(i) in therespective control algorithms for calculating the torque feedback valueTrq_fb and the basic local correction values Dktrq_bs_(i) frominterfering with each other to thereby prevent the integral terms fromexhibiting oscillating behaviors, and the absolute values of therespective integral terms from becoming very large. This makes itpossible to avoid improper modification of the correlation model. As aresult, the calculation accuracy of the basic local correction valuesDktrq_bs_(i), that is, the feedforward torque. Trq_ff can be enhanced,thereby making it possible to improve controllability in a transientstate. Further, if the absolute value of the immediately preceding valueDktrq_bs_(i)(k−1) of the basic local correction value is small, theforgetting coefficient λv is set to 1, and hence even when the torqueerror Etf has converged to 0, the torque feedback value Trq_fb can beheld at a proper value which is capable of compensating for thefollow-up error Et quickly. This makes it possible to enhance theresponsiveness of the air-fuel ratio control when the modified torqueerrors Wetrq_(i) start to increase.

On the other hand, the torque correction sensitivity-calculating section216 calculates a torque correction sensitivity Rtrq by searching a mapshown in FIG. 52 according to the engine speed NE and the non-drivewheel speed Ws_ref. Similarly to the above-described error weight Wt,the torque correction sensitivity Rtrq takes a value obtained bynormalizing a ratio ΔWs_act/ΔTrq between the amount ΔWs_act of change inthe drive wheel speed Ws_act and the amount ΔTrq of change in the enginetorque, with reference to the absolute value |ΔWs_act_ref/ΔTrq_ref| ofthe ratio ΔWs_act_ref/ΔTrq_ref obtained at the predetermined drive wheelspeed and the predetermined engine torque.

In FIG. 52, curves indicated by solid lines represent the values of thetorque correction sensitivity Rtrq, and curves indicated by broken linesrepresent the values of the above-described error weight Wt, forcomparison. As is clear from the comparison between the two curves, inthis map, the torque correction sensitivity Rtrq is set to haveapproximately the same tendency as that of the error weight Wt. Thereason for this is the same as given in the description of the FIG. 51map.

As described above, since the torque correction sensitivity Rtrq iscalculated by the same method as employed for the calculation of theerror weight Wt, the torque correction sensitivity Rtrq is calculated asa value indicative of the degree of the influence of the maximum torqueTrq_max on the torque error Etf. Further, as described hereinabove, thedegree of the influence of the maximum torque Trq_max on the torqueerror Etf also varies with the gear ratio of the transmission, and hencein FIG. 52, the torque correction sensitivity Rtrq is set according tothe engine speed NE and the non-drive wheel speed Ws_ref.

Further, in FIG. 52, the torque correction sensitivity Rtrq is set to avalue equal to the value of the error weight Wt in a low non-drive wheelspeed region and at the same time in a low-to-medium engine speedregion, that is, in a region where the traction control is easy tooperate, and in the other regions, the torque correction sensitivityRtrq is set to a smaller value than the value of the error weight Wt.This is because when the amount of correction of the maximum torqueTrq_max by the torque correction value Ktrq in the decreasing directionis too small, there can occur slippage of the drive wheels. To avoidthis problem, the values of the torque correction sensitivity Rtrq areset as above.

The final value-calculating section 217 calculates local correctionvalues Dktrq_lc_(i) by the following equation (94), and then finallycalculates the torque correction value Ktrq by the following equation(95). It should be noted that in the present embodiment, the localcorrection values Dktrq_lc_(i) correspond the plurality of secondmultiplication values, and the plurality of multiplication values.

$\begin{matrix}{{{Dktrq\_ lc}_{i}(k)} = {{{{Rtrq}(k)} \cdot {{Wcv}_{i}(k)} \cdot {Dktrq\_ bs}_{i}}(k)}} & (94) \\{{{Ktrq}(k)} = {1 - {\sum\limits_{i = 1}^{t}{{Dktrq\_ lc}_{i}(k)}}}} & (95)\end{matrix}$

As shown in the above equation (95), the torque correction value Ktrq iscalculated by subtracting the total sum of the local correction valuesDktrq_lc_(i) from 1. This is because as described above, the torquecorrection value Ktrq is used as a multiplication value by which themaximum torque Trq_max is multiplied, and hence when there is no need tocorrect the maximum torque Trq_max, the torque correction value Ktrq isthus calculated to make Ktrq equal to 1.

As described hereinabove, the control apparatus 1B according to thepresent embodiment calculates the engine torque Trq by the tractioncontroller 200, and although not shown, carries out the variablemechanism control process, the air-fuel ratio control process, and theignition timing control process so as to obtain the engine torque Trq.

Next, a description will be given of control results obtained when thetraction control is performed by the control apparatus 1B according tothe third embodiment configured as described above. FIG. 53 shows anexample of control results obtained by the control apparatus 1B when theacceleration/deceleration of the vehicle is repeatedly performed on aroad surface having a small frictional resistance. The above exampleillustrates control results obtained by using basic local correctionvalues composed of the elements of three values as the basic localcorrection values Dktrq_bs_(i) for ease of understanding. Further, FIG.54 shows, for comparison with the FIG. 53 example, an example(hereinafter referred to as “the comparative example”) of controlresults obtained when the torque correction value Ktrq is held at 1,i.e. when the maximum torque Trq_max is directly used as the correctedmaximum torque Trq_max_mod.

Referring to FIGS. 53 and 54, when a comparison is made between theexample and the comparative example as to changes in the feedforwardtorque Trq_ff and the torque feedback value Trq_fb within a time periodfrom the start of acceleration through the start of deceleration(between time points t1 and t2, t3 and t4, t11 and t12, and t13 andt14), it is understood that the two values Trq_ff and Trq_fb are bothmade smaller in the example according to the present embodiment than inthe comparative example, whereby the present embodiment is enhanced incontrollability.

Further, when another comparison is made between the example and thecomparative example as to changes in the drive wheel speed Ws_act withrespect to those in the target wheel speed Ws_cmd after the start of thedeceleration, it is understood that the degree of deviation of the drivewheel speed Ws_act from the target wheel speed Ws_cmd, i.e. the controlerror is suppressed to a smaller value in the example of the controlresults according to the present embodiment than in the comparativeexample, whereby the present embodiment is enhanced in the controlaccuracy.

As described hereinabove, according to the control apparatus 1B of thethird embodiment, the torque feedback value Trq_fb corresponding to thecontrol error is calculated according to the drive wheel speed Ws_actand the target wheel speed Ws_cmd; the torque error Etf is calculated asthe difference between the torque feedback value Trq_fb and the targettorque feedback value Trq_fb_cmd; the link weight functions Wcv_(i) arecalculated by searching the FIG. 50 map according to the engine speedNE; and the modified torque errors Wetrq_(i) are calculated bymultiplying the torque error Etf by the error weight Wt and the linkweight functions Wcv_(i).

Further, the basic local correction values Dktrq_bs_(i) are calculatedsuch that the modified torque errors Wetrq_(i) calculated as above arecaused to converge to 0 (i.e. such that the torque feedback value Trq_fbis caused to converge to the target torque feedback value Trq_fb_cmd),and the local correction values Dktrq_lc_(i) are calculated bymultiplying the basic local correction values Dktrq_bs_(i) by the torquecorrection sensitivity Rtrq and the link weight functions Wcv_(i). Then,the torque correction value Ktrq is calculated by subtracting the totalsum of the local correction values Dktrq_lc_(i) from 1, and thefeedforward torque Trq_ff is calculated using the corrected maximumtorque Trq_max_mod obtained by correcting the maximum torque Trq_max bythe torque correction value Ktrq, and the equation (71).

More specifically, since the feedforward torque Trq_ff is calculatedusing the correlation model modified such that the torque error Etfbecomes equal to 0, the torque error Etf, i.e. the control error can beproperly compensated for just enough by the thus calculated feedforwardtorque Trq_ff, even under a condition where the correlation between themaximum torque Trq_max and the feedforward torque Trq_ff is changed byunpredictable changes of conditions other than disturbance, such as ageddegradation of output characteristics of the engine 3, variationsbetween individual engines, changes in the degrees of abrasion of tires,and changes in the frictional resistance of road surfaces, causing thetorque error Etf, i.e. the slippage of the drive wheels to be liable totemporarily increase.

In addition thereto, the feedforward torque Trq_ff is calculated usingthe equation (71) expressing the correlation between the correctedmaximum torque Trq_max_mod and the feedforward torque Trq_ff, so thatthe slippage of the drive wheels can be compensated for more quicklythan in a case where the slippage of the drive wheels is compensated forby the torque feedback value Trq_fb calculated with a feedback controlalgorithm. As described above, even under the condition where anincrease in the torque error Etf, i.e. the slippage of the drive wheelsis temporarily caused by the change in the correlation between themaximum torque Trq_max and the feedforward torque Trq_ff, it is possibleto compensate for the slippage of the drive wheels properly and quickly,thereby making it possible to ensure higher-level control accuracy ofthe wheel speeds than a gain schedule correction (or modification)method. In short, a high-level traction control can be realized.

Further, the modified torque errors Wetrq_(i) are calculated bymultiplying the torque error Etf by the error weight Wt and the linkweight functions Wcv_(i), and as described above, the four link weightfunctions Wcv_(i) are calculated in a manner such that they areassociated with the four regions within which the engine speed NE isvariable. The four link weight functions Wcv_(i) are set to positivevalues not larger than 1 in the regions associated therewith, and inregions other than the associated regions, they are set to 0, while thesum of the values of the link weight functions Wcv_(i) associated withregions overlap each other are set to be equal to the maximum value of 1of each of the link weight functions Wcv_(i). This makes it possible todistribute the torque error Etf to the four basic local correctionvalues Dktrq_bs_(i) via the values of the four link weight functionsWcv_(i), whereby it is possible to properly reduce the degree ofdeviation of the correlation model in each of the four regions.Particularly even when the deviation of the correlation model from theactual correlation between the maximum torque Trq_max and thefeedforward torque Trq_ff is different in the direction of a change inthe deviation in each of the four regions of the engine speed NE, it ispossible to properly modify the correlation model on an region-by-regionbasis while coping with the deviation.

Further, the local correction values Dktrq_lc_(i) are calculated bymultiplying the basic local correction values Dktrq_bs_(i) by the torquecorrection sensitivity Rtrq and the link weight functions Wcv_(i), andthe torque correction value Ktrq is calculated by subtracting the totalsum of the local correction values Dktrq_lc_(i) from 1. This makes itpossible to calculate the torque correction value Ktrq as a valueobtained by a successive combination of the four basic local correctionvalues Dktrq_bs_(i). Thus, even when the engine speed NE suddenlychanges in a state in which the four basic local correction valuesDktrq_bs_(i) are different from each other, the torque correction valueKtrq can be calculated such that it can change continuously in astepless manner according to the sudden change in the engine speed NE.

Therefore, by using the corrected maximum torque Trq_max_mod obtained bycorrecting the maximum torque Trq_max by the thus calculated torquecorrection value Ktrq (i.e. by modifying the correlation model), thefeedforward torque Trq_ff can be calculated such that it changes in asmooth and stepless manner even when the engine speed NE is suddenlychanged by a sudden change in the accelerator pedal opening AP. As aresult, even under a condition where the torque error Etf, i.e. theslippage of the drive wheels is liable to temporarily increase due to asudden change in the engine speed NE, it is possible to avoid a suddenimproper change or a sudden stepped change in the engine torque Trq,thereby making it possible to enhance the accuracy and stability ofcontrol.

Further, the error weight Wt is calculated such that it reflects thedegree of influence of the non-drive wheel speed Ws_ref and the enginespeed NE on the torque error Etf, and hence by using the thus calculatederror weight Wt, the feedforward torque Trq_ff can be calculated as avalue reflecting the degree of influence of the non-drive wheel speedWs_ref and the engine speed NE on the torque error Etf. In addition, thetorque correction sensitivity Rtrq is calculated as a value indicativeof the sensitivity of the maximum torque Trq_max to the torque errorEtf, so that by using the thus calculated torque correction sensitivityRtrq, it is possible to calculate the feedforward torque Trq_ff as avalue reflecting the sensitivity of the maximum torque Trq_max to thetorque error Etf. From the above, it is possible to enhance thecompensation accuracy of the feedforward torque Trq_ff for compensatingfor the torque error Etf, that is, the control error, thereby making itpossible to further enhance the control accuracy.

Further, in the algorithm [equations (73) to (83)] for calculating thetorque feedback value Trq_fb, and the algorithm [equations (86) to (93)]for calculating the basic local correction values Dktrq_bs_(i), theswitching function-setting parameters St and Sv are set to values whichsatisfy the relationship of −1<Sv<St<0. Therefore, the convergence rateof the modified torque errors Wetrq_(i) to 0 is lower than theconvergence rate of the follow-up error Et to 0, which prevents the tworesponse-specifying control algorithms from interfering with each other.This makes it possible to prevent the control system from exhibiting anoscillating behavior due to the interference between theresponse-specifying control algorithms, thereby making it possible toensure the stability of the control system.

It should be noted that although in the third embodiment, thefeedforward torque-calculating section 206 calculates the feedforwardtorque Trq_ff by the aforementioned equation (71), by way of example,the feedforward torque-calculating section 206 may be configured tocalculate the feedforward torque Trq_ff by the following equations (96)to (98) in place of the equation (71).Trq _(—) ff_temp(k)=Ktrq _(—)ap(k){Trq_max(k)−Ttrq_min(k)}+Ttrq_min(k)  (96)When Trq _(—) ff_temp(k)≦Trq_max_mod(k)Trq _(—) ff(k)=Trq _(—)ff_temp(k)  (97)When Trq _(—) ff_temp(k)>Trq_max_mod(k)Trq _(—)ff(k)=Trq_max_mod(k)  (98)

In the above equation (96), Trq_ff_temp represents the provisional valueof the feedforward torque. In this algorithm for calculating thefeedforward torque Trq_ff, as shown in the equations (97) and (98), alimiting process is performed on the provisional value Trq_ff_temp usingthe corrected maximum torque Trq_max_mod as an upper limit value,whereby the feedforward torque Trq_ff is calculated. Also when the aboveequations (96) and (98) are used as the algorithm for calculating thefeedforward torque Trq_ff, it is possible to obtain the sameadvantageous effects as provided by the use of the aforementionedequation (71).

Further, although in the third embodiment, the control algorithmexpressed by the aforementioned equations (86) to (93) is used as thealgorithm for calculating the basic local correction valuesDktrq_bs_(i), the basic local correction values Dktrq_bs_(i) may becalculated, in place of the above control algorithm, with a controlalgorithm expressed by the following equations (99) to (108), to whichare applied a combination of an adaptive disturbance observer and asliding mode control algorithm.

$\begin{matrix}{{\sigma\;{v_{i}(k)}} = {{{Wetrq}_{i}(k)} + {{Sv} \cdot {{Wetrq}_{i}\left( {k - 1} \right)}}}} & (99) \\{{{Urch\_ v}_{i}(k)} = {{{- {Krch\_ v}} \cdot \sigma}\;{v_{i}(k)}}} & (100) \\{{{Unl\_ v}_{i}(k)} = {{- {Knl\_ v}} \cdot {{sgn}\left( {\sigma\;{v_{i}(k)}} \right)}}} & (101) \\{{\sigma\; v_{i}{\_ hat}(k)} = {{{Urch\_ v}_{i}\left( {k - 1} \right)} + {{Unl\_ v}_{i}\left( {k - 1} \right)} + {{Uls\_ v}_{i}\left( {k - 1} \right)}}} & (102) \\\begin{matrix}{{{Ev\_ sig}_{i}(k)} = {{\sigma\;{v_{i}(k)}} - {\sigma\; v_{i}{\_ hat}(k)}}} \\{= {{\sigma\;{v_{i}(k)}} - {{Urch\_ v}_{i}\left( {k - 1} \right)} - {{Uls\_ v}_{i}\left( {k - 1} \right)}}}\end{matrix} & (103) \\{{{Uls\_ v}_{i}(k)} = {{{dUls\_ v}_{i}\left( {k - 1} \right)} + {{Uls\_ v}{\_ ini}}}} & (104) \\{{{dUls\_ v}_{i}(k)} = {{\lambda\;{v \cdot {dUls\_ v}_{i}}\left( {k - 1} \right)} + {\frac{Pv}{1 + {Pv}}{Ev\_ sig}_{i}(k)}}} & (105) \\{{{*{When}\mspace{14mu}{Dktrq\_ bs}{\_ L}} < {{Dktrq\_ bs}_{i}\left( {k - 1} \right)} < {{Dktrq\_ bs}{\_ H}}}{{\lambda\; v} = 1}} & (106) \\{{{*{When}\mspace{14mu}{Dktrq\_ bs}_{i}\left( {k - 1} \right)} \leqq {{Dktrq\_ bs}{\_ L}\mspace{14mu}{or}\mspace{14mu}{Dktrq\_ bs}{\_ H}} \leqq {{Dktrq\_ bs}_{i}\left( {k - 1} \right)}}{{\lambda\; v} = {\lambda\;{vlmt}}}} & (107) \\{{{Dktrq\_ bs}_{i}(k)} = {{{Urch\_ v}_{i}(k)} + {{Unl\_ v}_{i}(k)} + {{Uls\_ v}_{i}(k)}}} & (108)\end{matrix}$

In the above equation (102), σv_(i) _(—) hat represents an estimatedvalue of a switching function, and Uls_v_(i) represents a disturbanceestimated value. The disturbance estimated value Uls_v_(i) is calculatedwith a fixed gain identification algorithm to which is applied a δcorrecting method expressed by the equations (102) to (107). In theequation (103), Ev_sig_(i) represents an estimation error, and in theequation (104), Uls_v_ini represents the initial value of thedisturbance estimated value Uls_v_(i). Further, in the equation (104),dUls_v_(i) represents a modification term, and is calculated by theequations (105) to (107). In the equation (105), Pv represents a fixedidentification gain.

Further, as shown in the equation (108), the basic local correctionvalue Dktrq_bs_(i) is calculated as the sum of the reaching law inputUrch_v_(i), the non-linear input Unl_v_(i), and the disturbanceestimated value Uls_v_(i). It should be noted that the equations (102)to (107) express an algorithm with which the disturbance estimated valueUls_v_(i) of the adaptive disturbance observer is calculated.

According to the control algorithm configured as above, it is possibleto obtain the same advantageous effects as provided by the controlalgorithm expressed by the aforementioned equations (86) to (105). Morespecifically, in the equation (105), the immediately preceding valuedUls_v_(i)(k−1) of the modification term is multiplied by the forgettingcoefficient λv, and if the absolute value of the basic local correctionvalue Dktrq_bs_(i) is large, the forgetting coefficient λv is set to avalue within the range of 0<λ<1. Therefore, the aforementionedforgetting effect makes it possible to prevent the disturbance estimatedvalue Uls_v_(i) from being integrally increased, to thereby prevent thebasic local correction values Dktrq_bs_(i) form exhibiting an integralfluctuation behavior and an overshooting behavior. This makes itpossible to ensure the stability of the responsiveness of the controlsystem in a transient state. Further, if the absolute value of theimmediately preceding value Dktrq_bs_(i)(k−1) of the basic localcorrection value is small, the forgetting coefficient λv is set to 1,and hence even when the modified torque error Wetrq_(i) becomes close to0, the basic local correction values Dktrq_bs_(i) can be held at propervalues. This makes it possible to enhance the responsiveness of thecontrol system when the modified torque error Wetrq_(i) start toincrease, thereby making it possible to enhance the control accuracy.

In addition, the disturbance estimated value Uls_v_(i) is calculatedwith the fixed gain identification algorithm of the adaptive disturbanceobserver, to which is applied the δ correcting method, and hencecompared with the control algorithm according to the third embodimentwhich employs the adaptive law input Uadp_v_(i), it is possible tofurther enhance the capability of suppressing the integral fluctuationbehavior and the overshooting behavior of the basic local correctionvalues Dktrq_bs_(i).

Further, although in the third embodiment, the link weight functionsWcv_(i) are used as the plurality of predetermined functions, by way ofexample, the plurality of predetermined functions in the presentinvention are not limited to these, but any suitable functions may beused insofar as they are associated with a plurality of regions formedby dividing a region where the reference parameter is variable,respectively, and set to values other than 0 only in the associatedregions while being set to 0 in regions other than the associatedregions, such that in regions overlapping each other, the absolute valueof the total sum of the values of functions associated with theoverlapping regions becomes equal to the absolute value of the maximumvalue of each function. For example, link weight functions Wcv_(ij) maybe calculated by using a map in which the above-described “valve liftLiftin” is replaced by the “non-drive wheel speed Ws_ref” in FIG. 42, tothereby use such that the non-drive wheel speed Ws_ref are used the linkweight functions Wcv_(ij) as the plurality of predetermined functions.Also when the link weight functions Wcv_(ij) thus calculated are used,it is possible to obtain the same advantageous effects as provided bythe FIG. 42 link weight functions Wcp_(ij) according to the secondembodiment.

Further, although in the third embodiment, the engine speed NE is usedas the reference parameter, by way of example, the reference parameteraccording to the present invention is not limited to this, but anysuitable parameters may be used insofar as they are parameters otherthan the drive wheel speed Ws_act as the controlled variable. Forexample, three kinds of parameters, such as the non-drive wheel speedWs_ref, the engine speed NE, and the maximum torque Trq_max, may be usedfor reference parameters to calculate the values of the link weightfunctions Wcv_(i) according thereto, or two of them, i.e. the enginespeed NE and the maximum torque Trq_max may be used as referenceparameters to calculate the values of the link weight functions Wcv_(i)according thereto.

Further, although in the third embodiment, the feedforward torque Trq_ffis calculated using the equations (70) and (71) as the correlationmodel, by way of example, the correlation model for use in calculationof the feedforward torque Trq_ff is not limited to this, but any othersuitable calculating equations and maps may be used. For example, thefeedforward torque Trq_ff may be calculated using an equation in whichthe corrected maximum torque Trq_max_mod and the normalization demanddriving force Ktrq_ap in the equation (71) are replaced by the maximumtorque Trq_max and a value Ktrq·Ktrq_ap, respectively. Further, thefeedforward torque Trq_ff may be calculated using an equation in whichthe corrected maximum torque Trq_max_mod and the normalization demanddriving force Ktrq_ap in the equation (71) are replaced by the maximumtorque Trq_max and a value which is obtained by performing a limitingprocess using the torque correction value Ktrq as an upper limit valueon the normalization demand driving force Ktrq_ap, respectively.

Further, although in the third embodiment, the error weight Wt iscalculated by searching the FIG. 51 map according to the engine speed NEand the non-drive wheel speed Ws_ref, by way of example, the method ofcalculating the error weight Wt is not limited to this. For example, inplace of the map shown in FIG. 51, there may be used a map in which thevalue of the error weight Wt is set in advance with respect to theaverage value of the drive wheel speed Ws_act and the non-drive wheelspeed Ws_ref, and the engine speed NE. Further, a map may be used inwhich each of values of the error weight Wt is set in advance withrespect to a larger (or smaller) one of the drive wheel speed Ws_act andthe non-drive wheel speed Ws_ref, and the engine speed NE. Furthermore,a map may be used in which each value of the error weight Wt is set inadvance with respect to the target wheel speed Ws_cmd and the enginespeed NE.

Furthermore, although in the third embodiment, the maps shown in FIGS.51 and 52 are used when the error weight Wt and the torque correctionsensitivity Rtrq are calculated during the traction control of theengine 3 with the automatic transmission, by way of example, this is notlimitative, but when traction control is carried out for an engine witha manual transmission, or for an engine with a so-called automatic MT inwhich an actuator instead of a manual operating force performs the speedvarying operation, in place of the maps shown in FIGS. 51 and 52, theremay be used a plurality of two-dimensional maps (i.e. tables) in whichthe values of the error weight Wt and the torque correction sensitivityRtrq are set in advance with respect to the engine speed NE on a gearratio-by-gear ratio basis, respectively.

Further, although in the third embodiment, the torque correctionsensitivity Rtrq is calculated using the FIG. 52 map, by way of example,this is not limitative, but the torque correction sensitivity Rtrq maybe calculated using the FIG. 51 map in place of the FIG. 52 map. Thatis, the torque correction sensitivity Rtrq may be calculated as a valueequal to the weight error Wt. In addition, in the equation (94), thetorque correction sensitivity Rtrq may be set to 1 such thatDktrq_lc_(i)=Dktrq_bs_(i) holds.

Further, although in the first and second embodiments, the controlapparatus according to the present invention is applied to a controlapparatus which carries out air-fuel ratio control, and in the thirdembodiment, the control apparatus according to the present invention isapplied to a control apparatus which carries out traction control, byway of example, this is not limitative, but it may be applied to anysuitable control apparatuses for various industrial apparatuses, whichcalculates a first input value for feedforward control of a controlledvariable, according to reference parameters, by using a correlationmodel representative of the correlation between the reference parametersand the first input value, calculates a second input value for use inperforming feedback control of the controlled variable such that thecontrolled variable is caused to converge to a target controlledvariable, with a predetermined feedback control algorithm, andcalculates a control input based on the first input value and the secondinput value.

Furthermore, although in the first to third embodiments, themodification values (correction values) for modifying the referenceparameters are calculated so as to modify the correlation model, by wayof example, modification values for modifying the first input value maybe calculated with the control algorithms according to the first tothird embodiments.

It is further understood by those skilled in the art that the foregoingare preferred embodiments of the invention, and that various changes andmodifications may be made without departing from the spirit and scopethereof.

1. A control apparatus for controlling a controlled variable of acontrolled object by a control input, comprising: controlledvariable-detecting means for detecting the controlled variable;reference parameter-detecting means for detecting a reference parameterof the controlled object other than the controlled variable of thecontrolled object; target controlled variable-setting means for settinga target controlled variable serving as a target to which the controlledvariable is controlled; and control input-calculating means forcalculating a first input value for feedforward control of thecontrolled variable, according to the reference parameter, using acorrelation model representative of a correlation between the referenceparameter and the first input value, calculating a second input valuefor performing feedback control of the controlled variable such that thecontrolled variable is caused to converge to the target controlledvariable, with a predetermined feedback control algorithm, andcalculating the control input based on the first input value and thesecond input value, wherein said control input-calculating meanscomprises: error parameter-calculating means for calculating an errorparameter indicative of a control error to be compensated for by thefirst input value, based on the controlled variable and the targetcontrolled variable; model-modifying means for calculating a pluralityof modification values respectively associated with a plurality ofregions formed by dividing a region within which the reference parameteris variable, with a predetermined control algorithm, such that the errorparameter becomes equal to a predetermined target value, and modifyingthe correlation model using the plurality of modification values; andfirst input value-calculating means for calculating the first inputvalue using the modified correlation model.
 2. A control apparatus asclaimed in claim 1, wherein said reference parameter-detecting meansdetects a plurality of reference parameters as the reference parameter,wherein the correlation model is configured such that the correlationmodel is representative of a relationship between the plurality ofreference parameters and the first input value, and wherein saidmodel-modifying means calculates the plurality of modification valuessuch that the plurality of modification values are associated with aregion within which at least one of the plurality of referenceparameters is variable.
 3. A control apparatus as claimed in claim 1,wherein said model-modifying means calculates a plurality of firstmultiplication values by multiplying a difference between the errorparameter and the predetermined target value, by values of a respectiveplurality of predetermined functions, and calculates the plurality ofmodification values according to the plurality of first multiplicationvalues, respectively, wherein the plurality of regions have adjacentregions overlapping each other, and wherein the plurality ofpredetermined functions are associated with the plurality of regions,respectively, and are set to values other than 0 only in the associatedregions and to 0 in regions other than the associated regions, such thatin regions overlapping each other, an absolute value of a total sum ofvalues of the respective functions associated with the overlappingregions becomes equal to an absolute value of a maximum value of thefunctions.
 4. A control apparatus as claimed in claim 3, wherein saidmodel-modifying means calculates a plurality of second multiplicationvalues by multiplying the plurality of modification values by values ofthe respective plurality of predetermined functions, respectively, andmodifies the correlation model using a total sum of the plurality ofsecond multiplication values.
 5. A control apparatus as claimed in claim1, wherein said model-modifying means calculates a plurality ofmultiplication values by multiplying the plurality of modificationvalues by values of a respective plurality of predetermined functions,respectively, and modifies the correlation model using a total sum ofthe plurality of multiplication values, wherein the plurality of regionshave adjacent regions overlapping each other, and wherein the pluralityof predetermined functions are associated with the plurality of regions,respectively, and are set to values other than 0 only in the associatedregions and to 0 in regions other than the associated regions, such thatin regions overlapping each other, an absolute value of a total sum ofvalues of the respective functions associated with the overlappingregions becomes equal to an absolute value of a maximum value of thefunctions.
 6. A control apparatus as claimed in claim 1, wherein thecontrolled object is an internal combustion engine in which an amount ofintake air drawn into a cylinder of the engine is changed by a variableintake mechanism, as desired, the controlled variable being an air-fuelratio of a mixture in the engine, the control input being an amount offuel to be supplied to the engine, the reference parameter including atleast one of an operating condition parameter indicative of an operatingcondition of the variable intake mechanism, and a rotational speed ofthe engine.
 7. A control apparatus as claimed in claim 1, wherein thecontrolled object is a vehicle using the engine as a drive sourcethereof, the controlled variable being a first wheel speed of thevehicle, the control input being an output of the engine, the referenceparameter including at least one of a second wheel speed other than thefirst wheel speed, a limit value of the output of the engine, and arotational speed of the engine.
 8. A method of controlling a controlledvariable of a controlled object by a control input, comprising: acontrolled variable-detecting step of detecting the controlled variable;a reference parameter-detecting step of detecting a reference parameterof the controlled object other than the controlled variable of thecontrolled object; a target controlled variable-setting step of settinga target controlled variable serving as a target to which the controlledvariable is controlled; and a control input-calculating step ofcalculating a first input value for feedforward control of thecontrolled variable, according to the reference parameter, using acorrelation model representative of a correlation between the referenceparameter and the first input value, calculating a second input valuefor performing feedback control of the controlled variable such that thecontrolled variable is caused to converge to the target controlledvariable, with a predetermined feedback control algorithm, andcalculating the control input based on the first input value and thesecond input value, wherein said control input-calculating stepcomprises: an error parameter-calculating step of calculating an errorparameter indicative of a control error to be compensated for by thefirst input value, based on the controlled variable and the targetcontrolled variable; a model-modifying step of calculating a pluralityof modification values respectively associated with a plurality ofregions formed by dividing a region within which the reference parameteris variable, with a predetermined control algorithm, such that the errorparameter becomes equal to a predetermined target value, and modifyingthe correlation model using the plurality of modification values; and afirst input value-calculating step of calculating the first input valueusing the modified correlation model.
 9. A method as claimed in claim 8,wherein said reference parameter-detecting step includes detecting aplurality of reference parameters as the reference parameter, whereinthe correlation model is configured such that the correlation model isrepresentative of a relationship between the plurality of referenceparameters and the first input value, and wherein said model-modifyingstep includes calculating the plurality of modification values such thatthe plurality of modification values are associated with a region withinwhich at least one of the plurality of reference parameters is variable.10. A method as claimed in claim 8, wherein said model-modifying stepincludes calculating a plurality of first multiplication values bymultiplying a difference between the error parameter and thepredetermined target value, by values of a respective plurality ofpredetermined functions, and calculating the plurality of modificationvalues according to the plurality of first multiplication values,respectively, wherein the plurality of regions have adjacent regionsoverlapping each other, and wherein the plurality of predeterminedfunctions are associated with the plurality of regions, respectively,and are set to values other than 0 only in the associated regions and to0 in regions other than the associated regions, such that in regionsoverlapping each other, an absolute value of a total sum of values ofthe respective functions associated with the overlapping regions becomesequal to an absolute value of a maximum value of the functions.
 11. Amethod as claimed in claim 10, wherein said model-modifying stepincludes calculating a plurality of second multiplication values bymultiplying the plurality of modification values by values of therespective plurality of predetermined functions, respectively, andmodifying the correlation model using a total sum of the plurality ofsecond multiplication values.
 12. A method as claimed in claim 8,wherein said model-modifying step includes calculating a plurality ofmultiplication values by multiplying the plurality of modificationvalues by values of a respective plurality of predetermined functions,respectively, and modifying the correlation model using a total sum ofthe plurality of multiplication values, wherein the plurality of regionshave adjacent regions overlapping each other, and wherein the pluralityof predetermined functions are associated with the plurality of regions,respectively, and are set to values other than 0 only in the associatedregions and to 0 in regions other than the associated regions, such thatin regions overlapping each other, an absolute value of a total sum ofvalues of the respective functions associated with the overlappingregions becomes equal to an absolute value of a maximum value of thefunctions.
 13. A method as claimed in claim 8, wherein the controlledobject is an internal combustion engine in which an amount of intake airdrawn into a cylinder of the engine is changed by a variable intakemechanism, as desired, the controlled variable being an air-fuel ratioof a mixture in the engine, the control input being an amount of fuel tobe supplied to the engine, the reference parameter including at leastone of an operating condition parameter indicative of an operatingcondition of the variable intake mechanism, and a rotational speed ofthe engine.
 14. A method as claimed in claim 8, wherein the controlledobject is a vehicle using the engine as a drive source thereof, thecontrolled variable being a first wheel speed of the vehicle, thecontrol input being an output of the engine, the reference parameterincluding at least one of a second wheel speed other than the firstwheel speed, a limit value of the output of the engine, and a rotationalspeed of the engine.
 15. An engine control unit including a controlprogram for causing a computer to execute a method of controlling acontrolled variable of a controlled object by a control input, whereinthe control program causes the computer to detect the controlledvariable; detect a reference parameter of the controlled object otherthan the controlled variable of the controlled object; set a targetcontrolled variable serving as a target to which the controlled variableis controlled; and calculate a first input value for feedforward controlof the controlled variable, according to the reference parameter, usinga correlation model representative of a correlation between thereference parameter and the first input value, calculate a second inputvalue for performing feedback control of the controlled variable suchthat the controlled variable is caused to converge to the targetcontrolled variable, with a predetermined feedback control algorithm,and calculate the control input based on the first input value and thesecond input value, wherein when causing the computer to calculate thecontrol input, the control program causes the computer to calculate anerror parameter indicative of a control error to be compensated for bythe first input value, based on the controlled variable and the targetcontrolled variable; calculate a plurality of modification valuesrespectively associated with a plurality of regions formed by dividing aregion within which the reference parameter is variable, with apredetermined control algorithm, such that the error parameter becomesequal to a predetermined target value, and modifying the correlationmodel using the plurality of modification values; and calculate thefirst input value using the modified correlation model.
 16. An enginecontrol unit as claimed in claim 15, wherein the control program causesthe computer to detect a plurality of reference parameters as thereference parameter, wherein the correlation model is configured suchthat the correlation model is representative of a relationship betweenthe plurality of reference parameters and the first input value, andwherein the control program causes the computer to calculate theplurality of modification values such that the plurality of modificationvalues are associated with a region within which at least one of theplurality of reference parameters is variable.
 17. An engine controlunit as claimed in claim 15, wherein the control program causes thecomputer to calculate a plurality of first multiplication values bymultiplying a difference between the error parameter and thepredetermined target value, by values of a respective plurality ofpredetermined functions, and calculate the plurality of modificationvalues according to the plurality of first multiplication values,respectively, wherein the plurality of regions have adjacent regionsoverlapping each other, and wherein the plurality of predeterminedfunctions are associated with the plurality of regions, respectively,and are set to values other than 0 only in the associated regions and to0 in regions other than the associated regions, such that in regionsoverlapping each other, an absolute value of a total sum of values ofthe respective functions associated with the overlapping regions becomesequal to an absolute value of a maximum value of the functions.
 18. Anengine control unit as claimed in claim 17, wherein the control programcauses the computer to calculate a plurality of second multiplicationvalues by multiplying the plurality of modification values by values ofthe respective plurality of predetermined functions, respectively, andmodify the correlation model using a total sum of the plurality ofsecond multiplication values.
 19. An engine control unit as claimed inclaim 15, wherein the control program causes the computer to calculate aplurality of multiplication values by multiplying the plurality ofmodification values by values of a respective plurality of predeterminedfunctions, respectively, and modifying the correlation model using atotal sum of the plurality of multiplication values, wherein theplurality of regions have adjacent regions overlapping each other, andwherein the plurality of predetermined functions are associated with theplurality of regions, respectively, and are set to values other than 0only in the associated regions and to 0 in regions other than theassociated regions, such that in regions overlapping each other, anabsolute value of a total sum of values of the respective functionsassociated with the overlapping regions becomes equal to an absolutevalue of a maximum value of the functions.
 20. An engine control unit asclaimed in claim 15, wherein the controlled object is an internalcombustion engine in which an amount of intake air drawn into a cylinderof the engine is changed by a variable intake mechanism, as desired, thecontrolled variable being an air-fuel ratio of a mixture in the engine,the control input being an amount of fuel to be supplied to the engine,the reference parameter including at least one of an operating conditionparameter indicative of an operating condition of the variable intakemechanism, and a rotational speed of the engine.
 21. An engine controlunit as claimed in claim 15, wherein the controlled object is a vehicleusing the engine as a drive source thereof, the controlled variablebeing a first wheel speed of the vehicle, the control input being anoutput of the engine, the reference parameter including at least one ofa second wheel speed other than the first wheel speed, a limit value ofthe output of the engine, and a rotational speed of the engine.